Stanley Williams, a prisoner on California's death row, appeals the district court's denial of his 28 U.S.C. § 2254 habeas corpus petition challenging his 1981 conviction of multiple counts of first-degree murder and armed robbery and his sentence of death. Williams also appeals the district court's denial of his motion, made under Federal Rule of Civil Procedure 60(b), for relief from the court's judgment denying his habeas corpus petition. For the reasons set forth below, we affirm the district court's denial of Williams's habeas corpus petition, and we vacate the district court's order denying Williams's Rule 60(b) motion because the district court lacked jurisdiction to consider the motion.

I. The Trial.

On May 3, 1979, the state of California charged Williams with four counts of first-degree murder, three counts of robbery with the use of a firearm, one count of kidnapping, and eight special circumstances of robbery-murder and multiple murder. Williams's trial commenced on February 10, 1981. We respectfully take the following account of the trial, in large part, from the California Supreme Court decision in People v. Williams, 44 Cal.3d 1127, 245 Cal.Rptr. 635, 751 P.2d 901, 905-08 (1988) (en banc) ("Williams I"). We provide additional facts in the discussion, below, as necessary for consideration of Williams's claims for relief.

A. The Prosecution's Case.

The state presented evidence linking Williams to two separate incidents of murder and robbery. See Williams I, 245 Cal.Rptr. 635, 751 P.2d at 905-07. 1.

The 7-Eleven Murder and Robbery.

Alfred Coward, an immunized government witness, testified to the events leading to the murder of Albert Lewis Owens,1 an employee of a 7-Eleven store in Whittier, California. See id. at 905. Coward stated that at approximately 10:30 p.m. on February 27, 1979, Williams dropped by Coward's house. The two men then went to James Garrett's house, where Williams was staying. Only Williams went inside, returning with a sawed-off shotgun and accompanied by a man named Darryl. The three men made several stops, including one to obtain "Sherms," cigarettes containing phencyclidene ("PCP"). After sharing a Sherm, the three picked up Tony Simms. Williams then had a second Sherm with Coward and Simms, and asked Simms if he knew where they could "make money." See id.

Coward testified that, taking two cars, the four men made two unsuccessful restaurant and liquor-store robbery attempts. Subsequently, they went to a 7-Eleven where Owens was sweeping the parking lot. Simms and Darryl went into the store, followed by Owens, Williams, and Coward. Williams, the only one with a weapon, approached Owens and ordered him to keep walking. Owens walked toward the back rooms of the store with Williams and Coward following him. Williams instructed Owens to lie down, which he did. Williams shot out the store's television monitor and then shot and killed Owens. See id.

According to Coward, the four men returned to Simms's house where they divided among them the $120 that they had taken from the 7-Eleven cash register. When Simms asked Williams why he had shot Owens, Williams responded that he did not want to leave any witnesses. He also said that the shotgun shells could not be traced, and that he had retrieved a few of them. See id.

Coward saw Williams later that morning at Williams's brother's home. Williams told his brother about Owens, saying: "You should have heard the way he sounded when I shot him." Williams then made a growling noise and laughed hysterically for a number of minutes. See id.

2. The Brookhaven Motel Murders and Robbery.

Robert Yang and his family lived in and owned the Brookhaven Motel on South Vermont Street in Los Angeles, California. At about 5 a.m. on March 11, 1979, Yang heard a woman's screams and three or four shots. A few minutes later, he left his bedroom and saw that the door separating the motel office from the family's living quarters was ajar. The door seemed to have been forced open from the outside. Yang discovered his father, mother, and sister, all fatally wounded from shotgun fire. The cash drawer was open and empty. See id. at 906.

The police found two shotgun shell casings at the scene. A firearms expert testified that one of the shells could only have been fired from a weapon that Williams had purchased in 1974. See id.

Four witnesses provided testimony identifying Williams as a perpetrator of the Brookhaven Motel murders and robbery. Samuel Coleman, testifying as an immunized government witness, stated that on March 10, 1979 he and Williams went to the Showcase Bar, where Coleman remained until it closed around 6 a.m. Coleman last remembered seeing Williams at about 2:30 a.m. The next day, Williams told Coleman that he had robbed and killed some people on Vermont Street. Williams said that he had obtained approximately $50 from the robbery-murder and was going to use it to buy PCP. See id.

James Garrett testified that Williams kept some of his possessions at the Garrett house and stayed there approximately five days a week. Early on the morning of March 13, 1979, Williams told James Garrett and his wife that he had heard of the killing of some "Chinese people" on Vermont Street. Williams said that he did not know how the murders had occurred, but thought that the murderers were professionals because they had left no shells or witnesses at the scene. Williams also stated that he had heard that the killings had taken place at 5 a.m., and that two men had knocked down the door and taken $600. See id.

Williams later spoke to James Garrett a second time about the Brookhaven Motel murders and robbery. Williams described the incident, saying: "[A]fter the big guy knocked the door down, he went in the motel, and there was a guy laying on the couch, and he blew him away." Williams said that the man on the couch and a woman at the cash register were shot twice, and that another woman was also shot. James Garrett testified that Williams then indicated that he was the "big guy." See id.2

Esther Garrett confirmed the statements made by her husband. She testified that Williams informed them that the Brookhaven Motel murderers were using the money taken from the cash register to buy "juice," or PCP, and that they had picked up the shotgun shells so that there would be no evidence for the police. Williams also told Esther Garrett, outside the presence of her husband, that he, Williams, had committed the murders with his brother-in-law. See id.

George Oglesby, an inmate housed in the same cell block as Williams, testified that Williams admitted to shooting a man, a woman, and a child in the course of robbing a motel. See id. at 906-07. Oglesby also testified in detail to Williams's plan to escape from jail. Williams had invited Oglesby to participate in the plan, which was complete with drawings and involved an escape during a bus transfer from jail to court. See id. at 907. Two persons outside of jail were to disarm the officer driving the bus, and then Williams was to kill the person on the bus who planned to testify against Williams, as well as the two officers accompanying the bus. Williams later modified the plan to include blowing up the bus in order to prevent the authorities from quickly determining who had escaped. See id.

After receiving two notes from Williams relating information about outside participants in the escape plan, Oglesby informed Lieutenant Fitzgerald of the planned escape. Williams subsequently sent Oglesby more notes discussing the escape. See id.

The initial target date for the escape was June 12, 1979. However, Williams aborted the escape attempt planned for this day because he could not ensure that he and Oglesby would be transferred to court at the same time. In addition, after one of his court appearances, Williams informed Oglesby that the escape attempt had to be cancelled because Williams believed that two police vehicles had followed the bus transporting Williams between jail and court. Williams then altered the escape plan so that the escape attempt would occur after they left court. See id.

B. The Defense.

Williams presented an alibi defense. Beverly McGowan testified that she and Williams had dined and spent the night together on February 27, 1979, the night of Owens's murder. See id.

Fred Holiwell, Williams's stepfather, testified that he arrived at the Showcase Bar at around 3:30 a.m. on March 11, 1979, the morning of the Brookhaven Motel murders and robbery. He stated that he thought he saw Williams in the Showcase Bar parking lot area at about 5 a.m. Holiwell remembered seeing Williams at the Showcase Bar on this particular night because Williams had been involved in an altercation that resulted in a cut across Williams's chest. See id.

Eugene Riley, an inmate in the same cell block as Williams, testified that he saw Williams in the parking lot of the Showcase Bar at about 5 a.m. on March 11, 1979. Riley gave Williams a ride home at approximately 5:30 a.m. and said that Williams was smoking a Sherm at the time. See id.

Joseph McFarland, another inmate in Williams's cell block, provided testimony impeaching Oglesby's credibility. McFarland stated that Oglesby was a well-known "jailhouse rat," and that other inmates gave Oglesby false information because they knew him to be a government informant. See id. at 907-08. Through the use of cross-examination, defense counsel also brought out the motivations of the prosecution's witnesses to lie.

C. The Jury Verdict.

On March 13, 1981, the jury returned guilty verdicts against Williams on four counts of first-degree murder and two counts of robbery using a firearm.3 The jury also found to be true the eight special circumstances of robbery-murder and multiple murder. Following a penalty phase, at which neither the prosecution nor the defense put on any evidence, the jury returned a death sentence. On April 15, 1981, the trial court imposed a judgment of death.

II. The Appeal and Post-Conviction Proceedings.

Pursuant to California's 1978 death penalty law, Williams's conviction and sentence were automatically appealed to the California Supreme Court. While the appeal was pending, on June 25, 1984, Williams filed a state petition for a writ of habeas corpus, which was consolidated with his direct appeal. See id. at 905. The California Supreme Court ordered an evidentiary hearing on issues raised in the habeas corpus petition. An appointed referee conducted a five-day hearing and made factual findings on the issues of whether (1) Oglesby was a government agent that deliberately elicited incriminating statements from Williams in violation of the Sixth Amendment, (2) Oglesby was a government agent that interrogated Williams in violation of the Fifth Amendment, and (3) Williams's trial counsel was ineffective for failing to object to Oglesby's testimony under the Fifth and Sixth Amendments and correlative provisions of the California Constitution. See id. at 908. On April 11, 1988, the California Supreme Court issued an opinion affirming Williams's conviction and sentence and denying his habeas corpus petition. See id. at 921. The California Supreme Court denied Williams's petition for rehearing, and the United States Supreme Court denied his petition for a writ of certiorari. See Williams v. California, 488 U.S. 975, 109 S.Ct. 514, 102 L.Ed.2d 549 (1988).

On January 9, 1989, Williams filed a second state habeas corpus petition, which the California Supreme Court summarily denied. Williams filed a federal habeas corpus petition in the United States District Court for the Central District of California on January 23, 1989. The district court ordered the petition held in abeyance pending exhaustion of all of Williams's claims in state court.

On September 1, 1989, Williams filed a third state habeas corpus petition with the California Supreme Court, which ordered another evidentiary hearing on the question of whether the prosecution used Oglesby as a government agent in violation of Williams's Fifth and Sixth Amendment rights. See In re Williams, 7 Cal.4th 572, 29 Cal.Rptr.2d 64, 870 P.2d 1072, 1074 (1994) (en banc) ("Williams II"). After the second hearing and a post-hearing briefing, the California Supreme Court issued an opinion on April 11, 1994 that denied the habeas corpus petition. See id. at 1095. The Court also denied Williams's petition for rehearing. On June 21, 1995, the California Supreme Court denied Williams's fourth and final state habeas corpus petition on the merits and on procedural grounds.

After exhausting his claims in state court, Williams filed with the district court an amended federal habeas corpus petition on November 13, 1995. Granting, in part, the state's motion for summary judgment on March 27, 1998, the district court denied twenty-four of the twenty-eight claims raised in Williams's amended federal petition. See Williams v. Calderon, 48 F.Supp.2d 979, 1032 (C.D.Cal.1998) ("Williams III"). On May 27-28, 1998, the district court held an evidentiary hearing, at which witnesses were called and exhibits submitted, on Williams's claims that he was unconstitutionally shackled at trial and that his trial counsel rendered ineffective assistance in violation of the Sixth Amendment. See Williams v. Calderon, 41 F.Supp.2d 1043, 1046 (C.D.Cal. 1998) ("Williams IV"). The district court issued an opinion denying Williams's remaining claims on December 21, 1998, see id. at 1060-61, and entered judgment accordingly on December 23, 1998.

On January 8, 1999, Williams filed a motion asking the district court to amend its findings of fact and judgment under Federal Rules of Civil Procedure 52(b) and 59(e). While the motion to amend was still pending, on January 22, 1999, Williams noticed his intent to appeal the district court's December 23, 1998 judgment and also requested a certificate of probable cause ("CPC") in the event that the district court denied his motion to amend. On May 21, 1999, the district court did deny Williams's motion to amend, but granted his application for a CPC to appeal the denial of his federal habeas corpus petition. Williams filed an amended notice of appeal on June 3, 1999, indicating his intent to appeal the district court's order denying his motion to amend.

On November 17, 1999, Williams filed with the district court a motion for relief from judgment under Federal Rule of Civil Procedure 60(b), which the district court denied on December 17, 1999. On December 29, 1999, Williams noticed his intent to appeal the district court's order and requested a CPC for this purpose. The district court denied Williams's request on January 28, 2000. On February 10, 2000, Williams filed an amended notice of appeal, which we treated as an application to this court for a certificate of appealability ("COA"). On May 5, 2000, we granted a COA limited to the issues raised by the district court's denial of Williams's Rule 60(b) motion.

We first consider our jurisdiction over Williams's appeal of the district court's judgment denying his habeas corpus petition, No. 99-99018, and then of the district court's order denying his Rule 60(b) motion, No. 00-99001.

I. The Habeas Corpus Petition.

The district court had jurisdiction over Williams's habeas corpus petition under 28 U.S.C. § 2254. Williams filed a timely notice of appeal of the district court's December 23, 1998 judgment denying his petition. Williams's motion to amend under Rules 52(b) and 59(e), timely filed ten days after entry of the judgment, see Fed. R.Civ.P. 6(a), 52(b), 59(e), tolled the time to file his notice of appeal until May 21, 1999, when the district court issued its order denying the motion. See Fed. R.App. P. 4(a)(4)(A). Williams's January 22, 1999 notice of appeal also became effective on May 21, 1999, when the district court denied his motion to amend. See Fed. R.App. P. 4(a)(4)(B)(i); see also Schroeder v. McDonald, 55 F.3d 454, 458 (9th Cir.1995). Accordingly, Williams's notice of appeal was timely. See Fed. R.App. P. 4(a)(1)(A) & 4(a)(4)(A).

The CPC that the district court granted, however, is not sufficient to confer jurisdiction on this court to review the district court's denial of Williams's habeas corpus petition. Because Williams filed his notice of appeal after the effective date of the Anti-Terrorism and Effective Death Penalty Act ("AEDPA"), the AEDPA's provisions govern his right to appeal. See Slack v. McDaniel, 529 U.S. 473, 478, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000). Under the AEDPA, we cannot review a district court's final order in a habeas corpus proceeding without a COA, for which the petitioner must make "a substantial showing of the denial of a constitutional right" on each claim appealed. 28 U.S.C. § 2253(c); Mayfield v. Woodford, 270 F.3d 915, 921-22 (9th Cir.2001) (en banc). Because Williams could not have known that he needed a COA, rather than a CPC, to appeal the district court's denial of his habeas corpus petition, see Morris v. Woodford, 229 F.3d 775, 779 (9th Cir.2000) (noting that before the Supreme Court's decision in Slack, the rule in this circuit was that the AEDPA's provisions did not govern petitions filed in the district court before the AEDPA's effective date of April 24, 1996), we treat his notice of appeal as an application for a COA on the issues raised in his opening brief. See Cooper v. Calderon, 255 F.3d 1104, 1107 (9th Cir.2001); Schell v. Witek, 218 F.3d 1017, 1021 n. 4 (9th Cir.2000) (en banc).

The AEDPA's "substantial showing" requirement for a COA is "relatively low," Jennings v. Woodford, 290 F.3d 1006, 1010 (9th Cir.2002), and is satisfied when the "petitioner can `demonstrate that the issues are debatable among jurists of reason; that a court could resolve the issues [differently]; or that the questions are adequate to deserve encouragement to proceed further.'" Id. (quoting Barefoot v. Estelle, 463 U.S. 880, 893 n. 4, 103 S.Ct. 3383, 77 L.Ed.2d 1090 (1983)). "Although not dispositive, `[i]n a capital case, the nature of the penalty is a proper consideration in determining whether to issue a certificate of [appealability].'" Lambright v. Stewart, 220 F.3d 1022, 1025 (9th Cir.2000) (quoting Barefoot, 463 U.S. at 893, 103 S.Ct. 3383); see also Mayfield, 270 F.3d at 922. We resolve any doubt about granting a COA in the petitioner's favor. Jennings, 290 F.3d at 1010; Mayfield, 270 F.3d at 922; Petrocelli v. Angelone, 248 F.3d 877, 884 (9th Cir.2001).

Under the foregoing standard, we conclude that Williams has made the requisite "substantial showing of the denial of a constitutional right" on all but two of the claims presented in his opening brief in No. 99-99018. The two claims that do not warrant a COA are those that allege the prosecution's racially discriminatory use of peremptory challenges (Claim C), and the state's deliberate interference with Williams's confidential relationship with defense counsel and defense experts. (Claim AB)

Williams argues that under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), the prosecution impermissibly exercised peremptory challenges to exclude three African-American jurors in violation of the Equal Protection Clause. To establish a prima facie case, Williams must show that the facts and circumstances of the jury selection raise an inference of discriminatory exclusion by the prosecutor. See Batson, 476 U.S. at 96, 106 S.Ct. 1712. In his habeas corpus petition, Williams made only the following allegations regarding the facts and circumstances of voir dire: "The prosecutor used two of his nineteen peremptory challenges to remove the only two African-American females to be seated as prospective jurors.... He used one of three peremptory challenges to remove William Coleman, an African-American male, from potential jury service as an alternate juror in petitioner's case." In opposing the state's summary judgment motion, Williams failed to allege any additional facts or circumstances of the jury selection.

Although a pattern of strikes against African-Americans provides support for an inference of discrimination, id. at 97, 106 S.Ct. 1712, Williams must point to more facts than the number of African-Americans struck to establish such a pattern. We have previously stated that, "Using peremptory challenges to strike Blacks does not end the [prima facie] inquiry; it is not per se unconstitutional, without more, to strike one or more Blacks from the jury.... A district court must consider the relevant circumstances surrounding a peremptory challenge." United States v. Vasquez-Lopez, 22 F.3d 900, 902 (9th Cir.1994) (citations omitted).

Statistical facts like a high proportion of African-Americans struck and a disproportionate rate of strikes against African-Americans can establish a pattern of exclusion on the basis of race that gives rise to a prima facie Batson violation. See Fernandez v. Roe, 286 F.3d 1073, 1078 (9th Cir.2002) (prima facie case when the prosecutor struck four out of seven (57%) Hispanics, and 21% (four out of nineteen) of the prospective juror challenges were made against Hispanics who constituted only about 12% of the venire); Turner v. Marshall, 63 F.3d 807, 813 (9th Cir.1995) (five of nine (56%) African-Americans struck, and 56% (five out of nine) of the challenges were made against African-Americans who constituted only about 30% of the venire), overruled on other grounds by Tolbert v. Page, 182 F.3d 677 (9th Cir.1999) (en banc). However, because Williams failed to allege, and the record does not disclose, facts like how many African-Americans (apparently men, if any) sat on the jury, how many African-Americans were in the venire, and how large the venire was, it is impossible to say whether any statistical disparity existed that might support an inference of discrimination.

Williams attempts to create an inference of discrimination by pointing to (1) two, unrelated California Supreme Court decisions that found the prosecutor of Williams's case to have used peremptory challenges in a racially discriminatory manner in those cases, and (2) the prosecutor's closing argument at trial, in which Williams argues that the prosecutor made a racist analogy, a claim that the district court rejected and Williams does not appeal. We find these circumstances irrelevant because they are not "the circumstances concerning the prosecutor's use of peremptory challenges" at Williams's trial. Batson, 476 U.S. at 97, 106 S.Ct. 1712. Even if we assumed some relevance, the cited circumstances are not sufficient to raise an inference that the prosecutor exercised peremptory challenges in a racially discriminatory manner in Williams's case. Because Williams failed to present the district court with sufficient factual allegations to establish a prima facie case under Batson, we conclude that he has not made the requisite "substantial showing of the denial of a constitutional right," 28 U.S.C. § 2253(c)(2), and therefore deny a COA on his Batson claim.

We also decline a COA on Williams's claim that jailhouse monitoring of his conversations with visitors, and the interception by jail personnel of a document indicating the appointment of Dr. Alvin Davis as a defense psychiatrist, violated his Sixth Amendment right to counsel. When the government deliberately interferes with the confidential relationship between a criminal defendant and defense counsel, that interference violates the Sixth Amendment right to counsel if it substantially prejudices the criminal defendant. Clutchette v. Rushen, 770 F.2d 1469, 1471 (9th Cir.1985); Weatherford v. Bursey, 429 U.S. 545, 557-58, 97 S.Ct. 837, 51 L.Ed.2d 30 (1977). Substantial prejudice results from the introduction of evidence gained through the interference against the defendant at trial, from the prosecution's use of confidential information pertaining to defense plans and strategy, and from other actions designed to give the prosecution an unfair advantage at trial. United States v. Irwin, 612 F.2d 1182, 1187 (9th Cir.1980).

Even if we assume that the jailhouse monitoring and document interception were deliberate state interference with the confidential relationship between Williams and his counsel, Williams fails to establish substantial prejudice. Williams does not argue, and the record does not show, that the prosecution used any confidential information obtained from the monitoring or interception to achieve an unfair advantage at trial. In fact, the record indicates that the prosecution was unaware of the document regarding Dr. Davis's appointment until defense counsel brought it to the prosecution's and the trial court's attention. Rather, Williams contends that the monitoring and interception were prejudicial because they hampered his ability to present a defense of diminished mental capacity. Williams alleges that Dr. Davis refused to assist in the preparation of such a defense because the confidentiality of his appointment as a retained expert had been compromised, and because he was unable to obtain a confidential interview with Williams free of jailhouse monitoring.

The loss of Dr. Davis's services did not substantially prejudice Williams. Criminal defendants have no constitutional right to a psychiatrist of their choice, Ake v. Oklahoma, 470 U.S. 68, 83, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), and the trial court had already appointed three other mental-health experts to evaluate whether Williams was diminished in capacity at the time of the alleged offenses. Moreover, to obtain a fourth psychiatric opinion, defense counsel could have replaced Dr. Davis with another mental-health expert and sought an order from the trial court permitting a confidential interview. Williams fails to make a "substantial showing of the denial of a constitutional right" due to the state's jailhouse monitoring and document interception. See 28 U.S.C. § 2253(c)(2). We therefore deny a COA on Williams's claim that such monitoring and interception violated his Sixth Amendment right to counsel.

However, we conclude that Williams has made the requisite "substantial showing of the denial of a constitutional right" on the remaining claims presented in his opening brief in No. 99-99018, which we consider below on an issue-by-issue basis. See 28 U.S.C. § 2253(c)(3). We hereby grant a COA limited to these claims regarding the merits of Williams's habeas corpus petition.4 We exercise jurisdiction over the claims pursuant to 28 U.S.C. § 2253 and Rule 22 of the Federal Rules of Appellate Procedure.

II. The Rule 60(b) Motion.

We review de novo the district court's assertion of jurisdiction over Williams's Rule 60(b) motion for relief from judgment, see Carriger v. Lewis, 971 F.2d 329, 332 (9th Cir.1992) (en banc), and conclude that the court lacked jurisdiction to consider the motion. Once Williams filed his notice of appeal of the district court's judgment denying his habeas corpus petition, the district court lost jurisdiction over the petition. See id.; Gould v. Mutual Life Ins. Co., 790 F.2d 769, 772 (9th Cir.1986). To seek Rule 60(b) relief during the pendency of an appeal, "`the proper procedure is to ask the district court whether it wishes to entertain the motion, or to grant it, and then move this court, if appropriate, for remand of the case.'" Scott v. Younger, 739 F.2d 1464, 1466 (9th Cir.1984) (quoting Long v. Bureau of Econ. Analysis, 646 F.2d 1310, 1318 (9th Cir.), vacated on other grounds, 454 U.S. 934, 102 S.Ct. 468, 70 L.Ed.2d 242 (1981)). Because Williams did not observe the procedure required to revest the district court with jurisdiction to consider his Rule 60(b) motion, we conclude that the district court's December 17, 1999 order denying the motion is void for lack of jurisdiction. See Carriger, 971 F.2d at 332. We therefore vacate this order from which Williams appeals in No. 00-99001.

We review de novo the district court's denial of Williams's habeas corpus petition. See Turner v. Calderon, 281 F.3d 851, 864 (9th Cir.2002). The district court's partial grant of summary judgment in the state's favor is reviewed de novo. See Clark v. City of Lakewood, 259 F.3d 996, 1003 (9th Cir.2001). Summary judgment is appropriate if, viewing the evidence in the light most favorable to Williams, the non-moving party, (1) the district court correctly applied the relevant substantive law, and (2) there are no genuine issues of material fact in dispute. See id. at 1004. We review for an abuse of discretion the district court's denial of an evidentiary hearing and the scope of an evidentiary hearing held. Tapia v. Roe, 189 F.3d 1052, 1056 (9th Cir.1999); LaGrand v. Stewart, 133 F.3d 1253, 1270 (9th Cir.1998). The district court's findings of fact are reviewed for clear error. Turner, 281 F.3d at 864. Pure questions of law and mixed questions of law and fact, such as whether Williams received ineffective assistance of counsel, are reviewed de novo. See Mayfield, 270 F.3d at 922.

Because Williams filed his habeas corpus petition before the AEDPA's effective date, pre-AEDPA law applies to the merits of his petition. See id.; see also Slack, 529 U.S. at 481, 120 S.Ct. 1595. We presume that the state court's factual findings are correct unless Williams "did not receive a full, fair, and adequate hearing in the State court proceeding." 28 U.S.C. § 2254(d)(6) (West 1994); Silva v. Woodford, 279 F.3d 825, 835 (9th Cir.2002). Williams is entitled to a federal evidentiary hearing if (1) he has alleged facts that, if proven, would entitle him to habeas relief, and (2) he did not receive a full and fair opportunity to develop those facts in a state court. See Laboa v. Calderon, 224 F.3d 972, 981 n. 7 (9th Cir.2000); Phillips v. Woodford, 267 F.3d 966, 973 (9th Cir.2001). "Because of the limited scope of habeas corpus review, trial errors do not warrant relief unless the errors had substantial and injurious effect or influence in determining the jury's verdict." Turner, 281 F.3d at 864 (internal quotations omitted).

I. Guilt-Phase Challenges.

A. Excessive Security and Shackling at Trial. (Claim B)

Williams contends that he was unconstitutionally subjected to excessive security and shackling at trial. We consider each claim in turn.

1. Excessive Security.

Williams argues that the district court erred in denying his excessive security claim on summary judgment, see Williams III, 48 F.Supp.2d at 996, because factual questions remained about the extent of the security measures taken at trial. Williams asks that we remand to the district court for an evidentiary hearing on his excessive security claim.5

In his habeas corpus petition, Williams asserted that "the obvious presence of more than the usual number of deputy sheriffs" violated his constitutional right to a fair trial. See Holbrook v. Flynn, 475 U.S. 560, 568, 106 S.Ct. 1340, 89 L.Ed.2d 525 (1986) (noting that "certain [courtroom] practices pose such a threat to the `fairness of the factfinding process' that they must be subjected to `close judicial scrutiny'") (quoting Estelle v. Williams, 425 U.S. 501, 503-04, 96 S.Ct. 1691, 48 L.Ed.2d 126 (1976)); Morgan v. Aispuro, 946 F.2d 1462, 1464 (9th Cir.1991) (certain courtroom arrangements prejudice the presumption of innocence). To support this claim, Williams relies upon a declaration by an alternate juror and comments made by his counsel at trial. Sherry Wiseman, an alternate juror, averred that because her brother had been a marshal, she knew that there were normally two bailiffs or marshals in court during trials. She stated that during Williams's trial, there were generally four marshals in the courtroom: one near Williams, one near the jury, and one on each side of the gate from the spectator section.

During trial, Joseph Ingber, Williams's counsel, made the following comments to the jury:

I just happened to glance around ... and found out that there were eight, sometimes nine deputy sheriffs sitting in this courtroom. Some uniform, some non-uniform. In any event, the entire trial has been permeated with bailiffs sitting immediately behind Mr. Williams, behind me, over my shoulder. Everywhere I have turned, there have [sic] been the protective hand of the Los Angeles County Sheriff making sure of something. I'm not sure what.

Aside from Wiseman's declaration and Ingber's comments, Williams cites to no other evidence or factual allegation to support his excessive security claim.

The noticeable deployment of security personnel in a courtroom during trial is not an inherently prejudicial practice that requires justification by an essential state interest specific to each trial. Holbrook, 475 U.S. at 568-69, 106 S.Ct. 1340; Morgan, 946 F.2d at 1464. Rather, in light of the variety of ways that security guards can be deployed, courts must determine prejudice on a case-by-case basis. Holbrook, 475 U.S. at 569, 106 S.Ct. 1340. In federal habeas corpus proceedings, federal courts reviewing the constitutionality of security personnel used at trial must "look at the scene presented to jurors and determine whether what they saw was so inherently prejudicial as to pose an unacceptable threat to defendant's right to a fair trial; if the challenged practice is not found inherently prejudicial and if the defendant fails to show actual prejudice, the inquiry is over." Id. at 572, 106 S.Ct. 1340; see also Ainsworth v. Calderon, 138 F.3d 787, 797 (9th Cir.1998).

The facts that Williams presents in his petition and through Wiseman's declaration and Ingber's trial comments do not permit a finding of actual prejudice. At most, only the assertion in Williams's petition — that "the obvious presence of more than the usual number of deputy sheriffs" deprived him of a fair trial — supports an inference of actual prejudice. However, conclusory allegations by counsel that are unsworn and unsupported by any proof or offer of proof do not provide an adequate basis to obtain a federal evidentiary hearing. Phillips, 267 F.3d at 973; Coleman v. McCormick, 874 F.2d 1280, 1284-85 (9th Cir.1989) (en banc) (citing Frazier v. United States, 335 U.S. 497, 503, 69 S.Ct. 201, 93 L.Ed. 187 (1948)). Thus, we must determine whether Williams's factual allegations support a conclusion that the deployment of security personnel at his trial was inherently prejudicial. The Supreme Court has said that security measures at trial are inherently prejudicial when they "tend[] to brand [the defendant] in [the jurors'] eyes with an unmistakable mark of guilt," Holbrook, 475 U.S. at 571, 106 S.Ct. 1340 (internal quotations omitted), or when they create "an unacceptable risk ... of impermissible factors coming into play." Id. at 570, 106 S.Ct. 1340 (quoting Williams, 425 U.S. at 505, 96 S.Ct. 1691); see also King v. Rowland, 977 F.2d 1354, 1358 (9th Cir.1992).

We hold that Williams's factual allegations are insufficient to justify a conclusion that the scene presented to the jurors was inherently prejudicial. Wiseman's declaration establishes only that she, an alternate juror, personally knew, due to her brother's experience as a marshal, that four marshals reflected additional security precautions. She did not indicate that any juror shared this knowledge or impression at trial.

Moreover, the placement of the four marshals, as Wiseman described it, does not create an unacceptable risk that the jurors impermissibly inferred Williams's guilt. As the Supreme Court has noted, "the presence of guards at a defendant's trial need not be interpreted as a sign that he is particularly dangerous or culpable.... If they are placed at some distance from the accused, security officers may well be perceived more as elements of an impressive drama than as reminders of the defendant's special status." Holbrook, 475 U.S. at 569, 106 S.Ct. 1340. According to Wiseman, only one of the marshals was near Williams, with the others near the jury and the spectators. The jurors might "just as easily [have] believe[d] that the [marshals were] there to guard against disruptions emanating from outside the courtroom or to ensure that tense courtroom exchanges [did] not erupt into violence." Id. (holding that the presence of four uniformed state troopers did not unconstitutionally deprive the defendant of a fair trial); see also Ainsworth, 138 F.3d at 797 (the use of four, and sometimes six, deputy sheriffs did not violate the defendant's right to a fair trial); King, 977 F.2d at 1358 (the use of three deputy sheriffs to guard the defendant was not improper).

Ingber's comments regarding the placement of eight or nine deputy sheriffs, some of which were in uniform and some of which were not, also fail to support a conclusion of inherent prejudice, warranting a federal evidentiary hearing. As already discussed, counsel's unsupported, unsworn, and conclusory allegations do not provide sufficient basis for an evidentiary hearing. Phillips, 267 F.3d at 973; Coleman, 874 F.2d at 1284-85.

Even assuming that Ingber's comments could provide a basis for an evidentiary hearing, his comments do not compel a different conclusion than the one we have reached based upon Wiseman's declaration because the comments do not necessarily present a different picture of Williams's trial than Wiseman's more specific account of the stations generally assumed by the four uniformed marshals. Although Ingber identified more security personnel than Wiseman, Ingber's count includes an undisclosed number of plain-clothed security guards. When security personnel are in plain clothes, they are not easily identified by jurors as guards and thus do not create the same risk of impermissible juror inferences. See Holbrook, 475 U.S. at 568-70, 572, 106 S.Ct. 1340 (addressing the risk of prejudice from the conspicuous, or at least noticeable, deployment of identifiable guards in uniform, and expressing "a preference that officers providing courtroom security in federal courts not be easily identifiable by jurors as guards"). Because the eight or nine deputy sheriffs that Ingber identified include plain-clothed guards, the scene that Ingber portrays is not necessarily any more inherently prejudicial than Wiseman's account of the four uniformed marshals at trial.

Any prejudice that Williams might have suffered from the presence of plain-clothed security guards at his trial cannot be attributed to inherently prejudicial courtroom procedures, but only to Ingber's statements calling the jury's attention to the guards' presence. Williams, however, cannot rely upon any prejudice from his trial counsel's statements implying extraordinary courtroom security measures to support his habeas claim that the security measures at trial impermissibly undermined the presumption of his innocence. See Morgan, 946 F.2d at 1465 (when defense counsel refused the opportunity to limit the implication that the security measures taken at trial were extraordinary, the petitioner could not use that decision to argue impermissible jury inferences).

We conclude that Williams has failed to allege facts that, if proven, would demonstrate that an excessive use of conspicuous security guards at his trial unconstitutionally deprived him of a fair trial. Accordingly, we decline Williams's request that we order an evidentiary hearing on his excessive security claim. See Laboa, 224 F.3d at 981 n. 7. The district court properly granted the state's motion for summary judgment on the claim.

2. Shackling.

Williams raises two arguments with respect to his shackling claim. First, he contends that the district court abused its discretion when it limited the scope of the evidentiary hearing on his shackling claim. He seeks remand to the district court for another hearing so that he can present additional oral testimony and cross-examine the state's witnesses. Second, Williams asserts that the district court's factual findings are not supported by the record, and that based upon these erroneous factual findings, the district court improperly concluded that the physical restraints used at trial were harmless error.6 See Williams IV, 41 F.Supp.2d at 1047-48.

(a) The Scope of the Evidentiary Hearing on Shackling.

In denying the state's motion for summary judgment on Williams's shackling claim, the district court stated that the "claim will be subject to the evidentiary hearing already scheduled in this case." Williams III, 48 F.Supp.2d at 995. Subsequently, the parties submitted exhibits and direct witness testimony via written declarations on the shackling claim, and the district court ordered the parties to brief the question of whether the claim's resolution required oral testimony in addition to the documents already in the record. After reviewing the record and the parties' briefs, the district court decided that the record did not require further supplementation with oral testimony. One of Williams's witnesses, however, refused to provide a written declaration. The district court allowed Williams to present oral testimony by this witness because it was not Williams's fault that he could not secure the declaration.

Williams argues that the district court abused its discretion when it restricted the evidence presented on his shackling claim to written declarations, for the most part, and limited oral testimony. Williams claims that the district court, in resolving his claim mostly on a written record, deprived him of a full evidentiary hearing, of the opportunity to present facts, and of the opportunity to cross-examine the state's witnesses.

We have previously held that a district court in a habeas corpus proceeding "need not conduct full evidentiary hearings," but may instead "expand the record ... with discovery and documentary evidence." Watts v. United States, 841 F.2d 275, 277 (9th Cir.1988) (per curiam) (denying a habeas corpus petitioner's contention that the district court erred in resolving a claim based on contradictory affidavits and interrogatories without an evidentiary hearing at which oral testimony could be provided). We stated that "[d]ecisions to hold hearings and conduct discovery in [habeas corpus] cases are committed to the [district] court's discretion." Id. The district court must only "give the prisoner's claim `careful consideration and plenary processing, including full opportunity for presentation of the relevant facts.'" Id. (quoting Blackledge v. Allison, 431 U.S. 63, 82-83, 97 S.Ct. 1621, 52 L.Ed.2d 136 (1977)).

Other circuits have similarly held that "there is a permissible intermediate step that may avoid the necessity of an expensive and time consuming hearing in every [habeas corpus] case. It may instead be perfectly appropriate, depending upon the nature of the allegations, for the district court to proceed by requiring that the record be expanded to include letters, documentary evidence, and, in an appropriate case, even affidavits." Chang v. United States, 250 F.3d 79, 86 (2nd Cir.2001) (finding no abuse of discretion when the district court dismissed the petitioner's claim without an evidentiary hearing with live witnesses) (citing Raines v. United States, 423 F.2d 526, 529-30 (4th Cir.1970)); see also Blackledge, 431 U.S. at 81-82, 97 S.Ct. 1621 ("[A]s is now expressly provided in the Rules Governing Habeas Corpus Cases, the district judge ... may employ a variety of measures in an effort to avoid the need for an evidentiary hearing.... In short, it may turn out ... that a full evidentiary hearing is not required."); Spreitzer v. Peters, 114 F.3d 1435, 1456 (7th Cir.1997) (same). In light of this case law, we conclude that it was within the district court's discretion to choose a middle path allowing the parties to present evidence through written declarations and limited oral testimony.

Williams, however, contends that the district court's denial of a full evidentiary hearing was an abuse of discretion because his cross-examination of the state's witnesses might have brought out defects in their written affidavits. Williams cites the Supreme Court's statement in Blackledge that "[w]hen the issue is one of credibility, resolution on the basis of affidavits can rarely be conclusive." Blackledge, 431 U.S. at 82 n. 25, 97 S.Ct. 1621 (internal quotations omitted). However, in construing Blackledge, our circuit and the Second Circuit have found no abuse of discretion when the district court "conclude[d] that [a full evidentiary] hearing would not offer any reasonable chance of altering its view of the facts." Chang, 250 F.3d at 86; Watts, 841 F.2d at 277 (finding that, in the case at hand, the issue of credibility could be conclusively decided on the basis of documentary testimony and evidence in the record). Such was the case here: the district court reviewed the declarations and exhibits already present in the record, considered the parties' arguments regarding the need for oral testimony and cross-examination, and concluded that this evidence would not alter the court's view of the record. The district court did not abuse its discretion in determining that oral testimony and cross-examination were not necessary because the documentary evidence submitted fully presented the relevant facts of Williams's shackling claim.

(b) The Merits of Williams's Shackling Claim.

A criminal defendant has a constitutional right to be free of shackles and handcuffs in the presence of the jury absent an essential state interest that justifies the physical restraints. Ghent v. Woodford, 279 F.3d 1121, 1132 (9th Cir.2002); Rhoden v. Rowland, 172 F.3d 633, 636 (9th Cir.1999). A claim of unconstitutional shackling is susceptible to harmless-error analysis, however. Duckett v. Godinez, 67 F.3d 734, 749 (9th Cir.1995); Castillo v. Stainer, 983 F.2d 145, 148 (9th Cir.1992), amended by 997 F.2d 669 (9th Cir.1993). An unjustified decision to restrain a defendant at trial requires reversal only if the shackles or handcuffs had "substantial and injurious effect or influence in determining the jury's verdict." Castillo, 997 F.2d at 669 (quoting Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)).

After conducting an evidentiary hearing on Williams's claim that his physical restraints at trial violated his right to due process, the district court denied the claim on the ground that the use of restraints was harmless error. See Williams IV, 41 F.Supp.2d at 1047-48. The district court based its decision on the following factual findings. Although a chain restrained Williams's legs during trial, no member of the jury saw the leg chain. Williams's hands were free of restraints during trial. However, on one occasion, a juror observed Williams in handcuffs with a coat draped over his handcuffed hands as he was being taken to or from the courtroom. No other juror saw Williams in handcuffs. See id. Williams challenges these factual findings underlying the district court's denial of his claim.

"Where there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous." Anderson v. Bessemer City, 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985). We give "due regard" to the district court's opportunity to judge the credibility of witnesses, see Fed.R.Civ.P. 52(a), and we will disturb the district court's credibility determinations or factual findings only when, "on the entire evidence," we are "left with the definite and firm conviction that a mistake has been committed." Easley v. Cromartie, 532 U.S. 234, 242, 121 S.Ct. 1452, 149 L.Ed.2d 430 (2001) (internal quotations omitted).

After reviewing the record, we conclude that none of the district court's factual findings are clearly erroneous. The bailiff to the trial judge provided detailed testimony about a thin, metal leg chain on Williams's ankles as he sat in court during trial. No juror indicated that Williams's legs were in restraints, however, and the bailiff stated that the jury was not able to view Williams's leg chain or feet under the defense table at trial. The bailiff also testified that Williams was brought into the courtroom and sat down at the defense table before the jury was allowed to enter, and that Williams was not allowed to stand until after the jury left. The penalty-phase jury foreman confirmed this procedure. Given this record, the district court did not clearly err in concluding that Williams's leg chain was not visible to the jury.

There also is no clear error in the district court's finding that Williams's hands were free of restraints in the courtroom. Williams disputes this factual finding, relying upon Juror Kellick's declaration in which she claimed to have seen Williams in handcuffs throughout the entire trial. The district court did not clearly err in disbelieving this declaration given that Juror Kellick averred in a later declaration that she had "vivid memories" of seeing Williams without handcuffs "lots of times," and particularly remembered him writing on a yellow pad. No other juror indicated observing Williams in handcuffs in the courtroom, and the bailiff testified that Williams was not handcuffed at any point in front of the jury.

One juror, however, testified that he recalled seeing Williams with his hands together, as though in handcuffs, and a coat draped over his likely handcuffed hands. The juror stated that he never actually saw the handcuffs around Williams's wrists, but inferred their existence based upon how Williams was holding his hands. In light of this testimony and the other evidence in the record, the district court did not clearly err in finding that the juror must have seen Williams in handcuffs as he was being brought to or from the courtroom.

Even if we assume that Williams's physical restraints at trial were unjustified, we conclude that the district court properly held that the error was harmless. When the jury never saw the defendant's shackles in the courtroom, we have held that the shackles did not prejudice the defendant's right to a fair trial. See Castillo, 997 F.2d at 669 (a waist chain that could not be seen by the jury was harmless error); Packer v. Hill, 291 F.3d 569, 583 (9th Cir.2002) (no prejudice resulted from the defendant's leg brace when no juror interviewed after trial remembered seeing a leg brace on the defendant); Rich v. Calderon, 187 F.3d 1064, 1069 (9th Cir.1999) (no prejudice when the ankle chains used at trial were not visible to the jury due to a curtain draped around the defense table); United States v. Collins, 109 F.3d 1413, 1418 (9th Cir.1997) (the defendant's leg shackles were harmless error because a curtain around the defense table hid the shackles from the jury's view). Thus, the use of the leg chain at Williams's trial was harmless error.

We have also held that a jury's brief or inadvertent glimpse of a defendant in physical restraints outside of the courtroom does not warrant habeas relief unless the petitioner makes an affirmative showing of prejudice. See Ghent, 279 F.3d at 1133 (the jurors' occasional, brief glimpses of the defendant in handcuffs and other restraints in the hallway at the entrance to the courtroom was not prejudicial); United States v. Olano, 62 F.3d 1180, 1190 (9th Cir.1995) ("a jury's brief or inadvertent glimpse of a defendant in physical restraints is not inherently or presumptively prejudicial to a defendant"); Castillo, 983 F.2d at 148 (no prejudice when, during transport to or from the courtroom, some members of the jury pool saw the defendant in shackles in the court corridor); United States v. Halliburton, 870 F.2d 557, 560-62 (9th Cir.1989) (jurors' inadvertent observation of the defendant in handcuffs in the corridor did not prejudicially impair the defendant's right to a fair trial); Wilson v. McCarthy, 770 F.2d 1482, 1485-86 (9th Cir.1985) (the jury's brief viewing of defendant's shackles as he left the witness stand at the conclusion of his testimony was not prejudicial). Accordingly, the juror's viewing of Williams in handcuffs with a coat draped over his handcuffed hands as he went to or from the courtroom was not inherently or presumptively prejudicial. Williams has made no showing of actual prejudice from this sighting, and as the district court noted, the fact that a coat covered Williams's handcuffs minimized any possible prejudice. See Williams IV, 41 F.Supp.2d at 1048. We therefore affirm the district court's denial of Williams's claim of unconstitutional shackling.

B. Samuel Coleman's Coerced Testimony. (Claim E)

Williams argues that the trial court's improper admission of Samuel Coleman's coerced testimony violated Williams's constitutional right to due process. Although Williams lacks standing to complain about infringements of Coleman's constitutional rights, see Rakas v. Illinois, 439 U.S. 128, 139-40, 99 S.Ct. 421, 58 L.Ed.2d 387 (1978), Williams is entitled to habeas relief if the trial court's admission of Coleman's testimony rendered the trial so fundamentally unfair as to violate due process. See Karis v. Calderon, 283 F.3d 1117, 1129 n. 5 (9th Cir.2002); Jeffries v. Blodgett, 988 F.2d 923, 934-35 (9th Cir.1993).

At trial, Coleman testified that Williams admitted to robbing and killing people on Vermont Street, which is where the Brookhaven Motel was located. Coleman also testified that Williams said that he had obtained approximately $50 from the robbery-murder, with which he planned to buy PCP. In a sworn declaration, subsequently presented in Williams's habeas corpus proceedings, Coleman attested to the following events. Williams and Coleman were driving in Coleman's car when the police stopped and arrested them both in 1979. At the city jail, police officers beat Coleman and then interrogated him, accusing him of having committed murder. In Coleman's words, "[t]he beating put so much fear into me — I was so terrorized and in so much pain physically — that I told the police just what they wanted to hear about Stanley." Then someone from the district attorney's office visited Coleman and informed him that the state would give him immunity if he testified against Williams. Coleman agreed because he feared further beatings and being charged with murder. The police arrested Coleman again in 1980 on an unrelated drug charge and said that he would get jail time on the charge if he did not testify against Williams. Coleman subsequently received a diversion sentence on the charge.

The district court correctly relied upon United States v. Mattison, 437 F.2d 84 (9th Cir.1970) (per curiam), in denying Williams's due process claim regarding Coleman's testimony. See Williams III, 48 F.Supp.2d at 1001. In Mattison, the appellant argued that a government witness's trial testimony was involuntary because the government had unconstitutionally interrogated the witness and created financial incentives for the witness to testify. Mattison, 437 F.2d at 85. Like Williams, the appellant contended that the trial court's admission of the involuntary testimony violated his right to due process. See id. In Mattison, we concluded, however, that the appellant's evidence of coercive interrogation and inducement to testify was insufficient to show that the witness's trial testimony was involuntary. We stressed that "[b]y the time of trial, the psychologically coercive atmosphere of that interrogation must surely have dissipated. There [was] no indication that [the witness] was told at any time by anyone what he should say on the witness stand." Id. We also noted that the witness was subject to cross-examination, through which the appellant brought out the facts of the interrogation and the inducement to testify, and that the jury was free to observe the witness's demeanor and gauge his credibility. Id. Because the alleged facts of coercive interrogation and inducement to testify did not support a conclusion that the witness's trial testimony was involuntary, we denied the appellant's due process claim. See id.

Williams's claim that Coleman's testimony at trial was involuntary depends upon (1) evidence that the police used illegal, coercive measures to interrogate him in 1979, and (2) evidence that the police induced him to testify in exchange for immunity in Williams's case and sentencing leniency on the 1980 drug charge. Williams does not allege that the prosecution introduced at trial any of Coleman's statements that were illegally obtained at Coleman's 1979 interrogation. Williams also does not claim that the state employed coercive tactics at the time of trial or immediately before trial in order to secure Coleman's trial testimony. Thus, as in Mattison, the question before us is whether the post-arrest coercion of a government witness so tainted that witness's trial testimony as to render the testimony's admission a violation of the defendant's right to due process.

An interrogating agent's suggestion that a suspect's cooperation with the government will have a positive effect on the suspect's possible sentence is not an improper inducement that causes the suspect's later testimony for the government to be involuntary. United States v. Leon Guerrero, 847 F.2d 1363, 1366 (9th Cir.1988); see also United States v. Moody, 778 F.2d 1380, 1384-85 (9th Cir.1985) (witness testimony provided pursuant to a plea agreement was not involuntary or coerced). Consequently, the statement by the police to Coleman, implying that Coleman would not receive jail time on his 1980 drug charge so long as he testified against Williams, did not render involuntary Coleman's trial testimony against Williams.

However, a promise of leniency accompanied by threats or other coercive practices constitutes improper influence and makes a subsequent inculpatory statement involuntary. See United States v. Tingle, 658 F.2d 1332, 1336 (9th Cir.1981) (the defendant's confession was involuntary when it was induced by an interrogating officer who accused the defendant of lying, recited the maximum penalties of crimes that could be charged, threatened the defendant that she might not see her two-year-old child if she went to prison, and promised the defendant that the agent would inform the prosecutor if she cooperated or refused to cooperate). Assuming the truth of Coleman's declaration, then the beatings, threatened murder charge, and offer of immunity in exchange for Coleman's testimony against Williams were coercive and rendered involuntary Coleman's statements incriminating Williams at the 1979 interrogation. See Leon Guerrero, 847 F.2d at 1366 (in assessing the voluntariness of an inculpatory statement, we must decide "whether, considering the totality of the circumstances, the government obtained the statement by physical or psychological coercion or by improper inducement so that the suspect's will was overborne").

In resolving whether the officers' coercion of Coleman at the 1979 interrogation so tainted his trial testimony as to render it involuntary, "[w]e must determine `whether, granting establishment of the primary illegality, the evidence to which ... objection is made has been come at by exploitation of that illegality or instead by means sufficiently distinguishable to be purged of the primary taint.'" Collazo v. Estelle, 940 F.2d 411, 421 (9th Cir.1991) (en banc) (quoting Maguire, EVIDENCE OF GUILT 221 (1959)). We look at factors like the passage of time between Coleman's illegal interrogation and his trial testimony, and whether intervening circumstances sufficiently insulated his testimony from the effect of the prior coercion. See Collazo, 940 F.2d at 421; Brown v. Illinois, 422 U.S. 590, 603-04, 95 S.Ct. 2254, 45 L.Ed.2d 416 (1975).

Applying these factors, we agree with the district court that Coleman's trial testimony was sufficiently voluntary. By the time Coleman testified at trial in 1981, approximately two years had passed since his illegal interrogation in 1979. With this passage of time, the physically and psychologically coercive atmosphere of the interrogation had certainly dissipated. See Mattison, 437 F.2d at 85 (the coercion of the witness's illegal post-arrest interrogation had dissipated by the time of trial); see also United States v. Lewis, 833 F.2d 1380, 1387-88 (9th Cir.1987) (any illegality in the first interrogation of the defendant following surgery did not taint her confession given 24 hours later). In addition, by the time of trial, Coleman was represented by counsel, who had negotiated Coleman's grant of immunity in Williams's case in exchange for Coleman's testimony against Williams.7 "With a lawyer present the likelihood that the police will practice coercion is reduced, and if coercion is nevertheless exercised the lawyer can testify to it in court." Cooper v. Dupnik, 963 F.2d 1220, 1240 (9th Cir.1992) (en banc). The record does not indicate that Coleman's attorney objected to coercive practices by the state at trial or in the negotiations regarding Coleman's immunity.

There is also no evidence that the admission of Coleman's trial testimony deprived Williams of a fair trial in violation of due process. Williams does not allege that Coleman's trial testimony was false, or that the state at any time instructed Coleman in how to inculpate Williams or in what to say on the witness stand. See Mattison, 437 F.2d at 85 (no evidence suggested that the government had coached the witness regarding his testimony). Williams did not lack the opportunity at trial to test the voluntariness and veracity of Coleman's testimony through cross-examination. According to Coleman's declaration, Williams knew that the police had beaten Coleman at the city jail. Thus, defense counsel might have cross-examined Coleman about the coercive police tactics employed at his 1979 interrogation. Coleman did disclose at trial the grant of immunity that he had received in exchange for his trial testimony, and defense counsel questioned him on the subject. The jury was therefore free to draw inferences regarding Coleman's credibility and motivations for testifying from the fact that he had entered into this bargain with the state. See id. (there was no violation of due process when the witness, who was previously illegally interrogated, was subject to cross-examination at trial through which the jury could assess the witness's credibility); Moody, 778 F.2d at 1384-85 (rejecting the argument that witness testimony pursuant to a plea agreement is so unreliable as to violate due process by pointing out that the witness's motivation for testifying can be explored through cross-examination). Finally, the fact that Coleman had counsel at Williams's trial provided some safeguard for the truth of Coleman's trial testimony. "The presence of a lawyer can ... help to guarantee that... a fully accurate statement [is given] to the police and that the statement is rightly reported by the prosecution at trial." Cooper, 963 F.2d at 1240.

Because Williams's argument regarding Coleman's trial testimony is essentially indistinguishable from that raised in Mattison, our decision in that case compels us to deny Williams's claim. Williams has not alleged sufficient facts to demonstrate that Coleman's trial testimony was involuntary and that its admission rendered Williams's trial so fundamentally unfair as to violate due process. We affirm the district court's grant of summary judgment on this claim.8

C. The Prosecution's Suppression of Material Evidence Favorable to the Defense. (Claims F & I)

Williams argues that the prosecution's failure to disclose material evidence impeaching the credibility of two key government witnesses violated his right to due process. In particular, Williams claims that the prosecution suppressed, and failed to correct false testimony regarding, a deal whereby the state procured the testimony of James Garrett in exchange for leniency in sentencing in an unrelated criminal case pending against Garrett.9 Williams also contends that the prosecution did not turn over two tapes in its possession that undermined the veracity of George Oglesby's testimony inculpating Williams. Williams asserts that the district court erred in granting the state's summary judgment motion on these claims, see Williams III, 48 F.Supp.2d at 1002-03, 1011-13, and requests remand for an evidentiary hearing on them.

Due process requires that the prosecution disclose to the defense evidence that is both favorable to the accused and material to guilt or punishment. United States v. Agurs, 427 U.S. 97, 107, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976); Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). The prosecution must turn over evidence impeaching its witnesses, Silva, 279 F.3d at 854; United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985), and also correct false testimony by its witnesses. Phillips, 267 F.3d at 984-85; California v. Trombetta, 467 U.S. 479, 485, 104 S.Ct. 2528, 81 L.Ed.2d 413 (1984). Evidence is material when there is "a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different. A `reasonable probability' is a probability sufficient to undermine confidence in the outcome." Bagley 473 U.S. at 682, 105 S.Ct. 3375; see also Karis, 283 F.3d at 1128.

1. The Undisclosed Deal with James Garrett. (Claim F)

The prosecution must disclose to the defense a government agreement with a witness that may motivate the witness to testify and that may affect the outcome of trial. Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). To prevail on his claim, Williams must first demonstrate the existence of an agreement whereby the state offered James Garrett leniency in sentencing in the criminal case pending against him in exchange for his testimony against Williams. See Williams v. Calderon, 52 F.3d 1465, 1475 (9th Cir.1995) (denying the petitioner's claim that the prosecution failed to disclose a deal with a testifying witness when the petitioner could not show the existence of the alleged deal).

The facts and circumstances that Williams alleges show only that James Garrett testified against Williams in the hope that his testimony would result in a reduced sentence in the criminal case against him. Williams's factual allegations are not sufficient to entitle him to habeas corpus relief because they do not establish the existence of the asserted agreement between the state and Garrett. See Williams, 52 F.3d at 1474-75 (no due process violation for failure to disclose an agreement with a testifying witness when the prosecution made no promises, and only suggested that the witness might receive a reduced penalty if he testified); Alderman v. Zant, 22 F.3d 1541, 1555 (11th Cir.1994) ("The simple belief by a defense attorney that his client may be in a better position to negotiate a reduced penalty should he testify ... is not an agreement within the purview of Giglio."). Accordingly, we do not remand for an evidentiary hearing because the district court properly granted summary judgment on Williams's claim that the state unconstitutionally suppressed its deal with James Garrett. See Laboa, 224 F.3d at 981 n. 7 (a federal evidentiary hearing requires the allegation of facts that, if proven, would warrant relief).

2. The Suppressed Tape Recordings. (Claim I)

The prosecution has a duty to turn over to the defense all exculpatory evidence material to guilt or punishment, including evidence affecting the credibility of witnesses whose testimony may be determinative of the trial outcome. Giglio, 405 U.S. at 154, 92 S.Ct. 763. Williams argues that the prosecution violated its duty by suppressing two tape recordings, one made in 1978 and the other in 1979, that undermine the credibility of Oglesby's trial testimony. Williams contends that the 1978 tape recording of a telephone conversation between Oglesby and prison inmate Leslie White shows them conspiring to fabricate testimony in an unrelated murder case. However, the California Supreme Court found otherwise.

After an evidentiary hearing conducted in conjunction with Williams's third state habeas corpus petition, the referee appointed by the California Supreme Court found that Lieutenant Fitzgerald, a member of the Los Angeles Sheriff's Office, made the 1978 tape recording at the request of Oglesby, who did not want to become entangled in White's purported scheme to escape from jail. Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1080. White's scheme was to implicate Oglesby in a crime in Ventura so that White, who was in custody in Los Angeles, could be transferred to Ventura to testify against Oglesby and attempt to escape from the Ventura jail. Id. Adopting these factual findings by the referee, the California Supreme Court declared that the 1978 tape recording "showed merely that Oglesby contacted Fitzgerald to secure his help when Oglesby thought that he was going to be `used' by, and falsely implicated by, Leslie White." Id. at 1079. Because we must defer to the California Supreme Court's factual findings on the 1978 tape recording, see 28 U.S.C. § 2254(d) (West 1994),10 we conclude that the recording is not exculpatory evidence that impeaches Oglesby's credibility. See Giglio, 405 U.S. at 154, 92 S.Ct. 763. Accordingly, the prosecution's failure to disclose the 1978 tape recording to the defense did not violate due process.

Williams also alleges that the prosecution improperly suppressed a 1979 tape recording of an interview between White and investigators for the Los Angeles district attorney's office, in which White asserts that Oglesby committed perjury when he testified in another, unrelated criminal case. Even assuming that this tape recording is the exculpatory impeachment evidence that Williams claims it to be,11 the recording is not material to Williams's guilt or punishment. See Bagley, 473 U.S. at 682, 105 S.Ct. 3375. Had the defense used the 1979 tape recording to undermine Oglesby's credibility, this evidence would have been merely cumulative of other evidence that the defense presented to impeach Oglesby. At trial, the defense effectively called into question the truthfulness of Oglesby's testimony through cross-examination. The defense elicited from Oglesby testimony showing, inter alia, that (1) he was an admitted murderer and accused rapist, (2) his plea agreement with the state drastically reduced his possible sentence on the charges against him, (3) he believed that his prior testimony for the state in an unrelated murder case would benefit him at sentencing, (4) he hoped to benefit further from his testimony against Williams, (5) he was a reputed "snitch," and (6) other inmates fed him fabricated information so that he would go to the authorities with it. In light of this evidence presented, the district court correctly determined that the 1979 tape recording "would not have cast [Oglesby] in a significantly worse light." Williams III, 48 F.Supp.2d at 1013. Because there exists no "reasonable probability that, had [the 1979 tape recording] been disclosed to the defense, the result of the proceedings would have been different," Bagley, 473 U.S. at 682, 105 S.Ct. 3375, we decline to remand for an evidentiary hearing, see Laboa, 224 F.3d at 981 n. 7, and affirm the district court's denial of this claim on summary judgment.

D. Improper Admission of Testimony of Government Agent George Oglesby. (Claims G & H)

In his state post-conviction proceedings, Williams argued that the trial court's admission of Oglesby's testimony violated the Sixth Amendment right to counsel because Oglesby was a government agent who deliberately elicited incriminating information from Williams in contravention of United States v. Henry, 447 U.S. 264, 100 S.Ct. 2183, 65 L.Ed.2d 115 (1980), and Massiah v. United States, 377 U.S. 201, 84 S.Ct. 1199, 12 L.Ed.2d 246 (1964). After two state evidentiary hearings on this claim, the California Supreme Court found that Oglesby did not act as a government agent prior to May 21, 1979, when Oglesby first informed law enforcement authorities about Williams's confession of criminal conduct and escape plans. The California Supreme Court then concluded that any impropriety in admitting evidence that Oglesby obtained from Williams after May 21, 1979 was harmless error because this post-May 21, 1979 evidence was cumulative of the evidence lawfully acquired before May 21, 1979. See Williams II, 29 Cal. Rptr.2d 64, 870 P.2d at 1087-88. The district court denied this claim on summary judgment, deferring to the California Supreme Court's factual findings and affirming its harmless-error analysis. See Williams III, 48 F.Supp.2d at 1003-11.

On appeal, Williams argues only that the two state evidentiary hearings on the factual issue of Oglesby's status as a government agent were not full and fair, and that the district court therefore improperly deferred to the California Supreme Court's factual findings. Under pre-AEDPA § 2254(d), we presume that the California Supreme Court's factual determinations are correct unless Williams demonstrates that he "did not receive a full, fair, and adequate hearing in the State court proceeding." 28 U.S.C. § 2254(d)(6) (West 1994); Silva, 279 F.3d at 835. Williams claims that the state hearings were not full and fair because (1) the prosecution suppressed material, exculpatory evidence at the first hearing, and (2) the prosecution and the state referee conducting the hearings refused to grant Williams's witnesses use immunity to testify at the second hearing, and these witnesses declined to testify, invoking their Fifth Amendment rights against self-incrimination.

Williams's first argument is without merit because at the second state hearing he presented the evidence that he claims the prosecution improperly suppressed. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1078. The second hearing therefore cured any inadequacy of the first due to the unavailability of the evidence that Williams identifies. Thus, we cannot conclude that any failure by the prosecution to disclose this evidence denied Williams a full, fair, and adequate hearing in state court. See 28 U.S.C. § 2254(d)(6) (West 1994).

With respect to Williams's second argument, we note that the prosecution's refusal to grant use immunity to a defense witness denies the defendant a fair trial only when (1) the witness's testimony would have been relevant, and (2) the prosecution refused to grant the witness use immunity with the deliberate intention of distorting the fact-finding process. See United States v. Westerdahl, 945 F.2d 1083, 1086 (9th Cir.1991); United States v. Lord, 711 F.2d 887, 891 (9th Cir.1983). To demonstrate the prosecutorial misconduct of the second prong, Williams must show that the prosecution intentionally caused a defense witness to invoke the Fifth Amendment right against self-incrimination, or that the prosecution granted immunity to a government witness in order to obtain that witness's testimony, but denied immunity to a defense witness whose testimony would have directly contradicted that of the government witness. See United States v. Duran, 189 F.3d 1071, 1087 (9th Cir.1999). We apply this due process standard to determine whether Williams was denied a full, fair, and adequate hearing in state court under pre-AEDPA § 2254(d)(6).

We will assume that Williams satisfies the "minimal requirement" that his witnesses' testimony would have been relevant to his Sixth Amendment claim. See United States v. Whitehead, 200 F.3d 634, 640 (9th Cir.2000) ("To satisfy the relevance prong, a defendant need not show that the testimony sought was either clearly exculpatory or essential to the defense; the testimony need be only relevant.") (internal quotations omitted). In the proceedings before the California Supreme Court, Williams argued that Leslie White would have provided testimony consistent with White's statements on the 1979 tape recording12 and in a 1989 declaration. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1090 n. 17. On the 1979 tape recording, White asserted that the Los Angeles police and district attorney's office engaged in illegal tactics to bolster weak prosecution cases. According to White, certain members of the police department and district attorney's office placed jailhouse informants, like White and Oglesby, in cells near a defendant's cell and encouraged them to obtain incriminating information from the defendant. If the defendant did not make any inculpatory statements, White alleged that the police officers or prosecutors forced the jailhouse informants to fabricate a confession of criminal conduct by the defendant. In the 1989 declaration, White claimed that Oglesby, at the behest of the police, fabricated his testimony regarding Williams's admission of responsibility for the Brookhaven Motel murders and robbery and regarding Williams's escape plans. Before the California Supreme Court, Williams also contended that witnesses Ferril Mickens, Larry Montez, and Steven Cisneros would have testified generally about jailhouse-informant practices and specifically about Oglesby's practices. See id. at 1092 n. 20. Assuming that Williams's witnesses would have testified as he claimed in state court,13 the witnesses' testimony would have been relevant to the factual question of whether and when Oglesby acted as a government agent and deliberately elicited incriminating statements from Williams.

Turning to the prosecutorial misconduct required under the second prong, we note that Williams does not contend that the prosecution granted immunity to its witnesses, while denying immunity to his witnesses, and nothing in the record supports an argument that the prosecution attempted to distort the fact-finding process in this manner. Thus, resolution of the second prong turns on whether the prosecution took affirmative steps to prevent Williams's witnesses from testifying. In deciding this matter, we rely upon the California Supreme Court's factual findings, which Williams does not contest, regarding his witnesses' refusals to testify. See 28 U.S.C. § 2254(d) (West 1994).

Two days before the rescheduled evidentiary hearing was set to begin, Leslie White was indicted and arrested for providing perjured testimony in past cases. One week later, after Williams called White as a witness, White asserted his Fifth Amendment right against self-incrimination and declined to testify. See Williams II, 29 Cal.Rptr.2d 64, 870 P.2d at 1090-91. When called to the stand, Ferril Mickens, Larry Montez, and Steven Cisneros also invoked their Fifth Amendment rights against self-incrimination and refused to testify. Williams's counsel had subpoenaed these three witnesses, but failed to secure protective orders for their transportation and housing during the evidentiary hearing. Mickens did not testify primarily because Williams and his counsel intimidated Mickens. Mickens feared that his testimony might result in bodily harm to himself or his family members. Montez declined to testify because he believed that his testimony would incriminate him and felt intimidated by Williams. Cisneros invoked his Fifth Amendment right for two reasons. First, given White's indictment, Cisneros feared that he might be indicted for perjury if he provided testimony helpful to Williams. Second, Cisneros feared for his safety during transportation and housing in the Los Angeles County jail system. See id. at 1092-93.

Based upon these factual findings and other evidence in the record, we conclude that the prosecution did not improperly cause Williams's witnesses to invoke their Fifth Amendment rights against self-incrimination. Undue prosecutorial interference in a defense witness's decision to testify arises when the prosecution intimidates or harasses the witness to discourage the witness from testifying, for example, by threatening the witness with prosecution for perjury or other offenses. United States v. Angiulo, 897 F.2d 1169, 1192 (1st Cir.1990); see also United States v. Morrison, 535 F.2d 223, 229 (3d Cir.1976) (the prosecutor's repeated statements to the defense witness about the dangers of perjury and self-incrimination and about the witness's right not to testify, culminating in a highly intimidating personal interview, improperly interfered with the witness's choice to testify and violated the defendant's right to due process); Lord, 711 F.2d at 891 (remanding for an evidentiary hearing on whether the prosecutor engaged in misconduct when the prosecutor told the defense witness about the self-incrimination privilege, said that the government would not prosecute the witness if he submitted to an interview and testified truthfully, and stated that any prosecution of the witness depended upon his testimony). The prosecution's conduct must amount to a substantial interference with the defense witness's free and unhampered determination to testify before the conduct violates the defendant's right to due process. United States v. Emuegbunam, 268 F.3d 377, 400 (6th Cir.2001); United States v. Pinto, 850 F.2d 927, 932 (2d Cir.1988).

No prosecutorial misconduct tainted White's decision not to testify at the second state hearing. The record does not support a conclusion that the prosecution brought baseless perjury charges against White to harass him and discourage him from testifying at the hearing. To the contrary, the record suggests that the charges were well-founded given White's admissions to the authorities that he had provided perjured testimony on a number of occasions. Moreover, the prosecution does not abuse its discretion when it refuses to grant use immunity to a defense witness who has been indicted or is the subject of a criminal investigation. See United States v. Croft, 124 F.3d 1109, 1117 (9th Cir.1997) ("declin[ing] to adopt a rule that would require the government to grant transactional immunity to an indicted co-conspirator, or to a more marginal witness indicted on related charges"); United States v. Condo, 741 F.2d 238, 239 (9th Cir.1984) (the denial of immunity for defense witnesses that were themselves the target of prosecutorial investigation did not deprive the defendant of a fair trial); accord Emuegbunam, 268 F.3d at 401; United States v. Cohen, 171 F.3d 796, 802 (3d Cir.1999); United States v. Mitchell, 886 F.2d 667, 669 670 (4th Cir.1989); United States v. Hooks, 848 F.2d 785, 802 (7th Cir.1988); United States v. Drape, 668 F.2d 22, 26 (1st Cir.1982). "While a grant of use immunity theoretically does not improve the legal position of the person immunized, in that he still can be prosecuted for his crime, in practice the burden placed on the government to prove that any evidence obtained against the immunized subject is not tainted by the suspect's statement can significantly impair future prosecutions" United States v. Thevis, 665 F.2d 616, 640 (5th Cir.1982). Williams sought White's testimony on how White, Oglesby, and other jailhouse informants fabricated testimony in criminal cases, the very subject of the perjury charges against White. Thus, the prosecution's refusal to grant White use immunity that could have jeopardized the state's case against White was not misconduct that rendered the state evidentiary hearing unfair.

We also find no indication that the prosecution improperly interfered in a decision by Mickens, Montez, or Cisneros to testify at the state hearing. Williams points to no direct communication between the prosecution and these witnesses on any subject. Compare Morrison, 535 F.2d at 229 (communication between the prosecutor and defense witness discouraged the witness from testifying); Lord, 711 F.2d at 891 (similar prosecutor-witness communication). Moreover, to the extent that White's per