Opinion by Judge RYMER; Opinion by Judge PAEZ; Dissent by Judge RYMER.

James F. Horton, II, a California state prisoner, appeals from the denial of his 28 U.S.C. § 2254 petition for a writ of habeas corpus. We agree with the magistrate judge’s analysis, adopted by the district court, and affirm on all issues except for Horton’s claim that his rights under Brady v. Maryland, 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963), were violated. As to that claim, the court reverses and remands in a separate opinion authored by Judge Paez.

I

Shortly after 2:30 p.m. on Monday, October 11, 1982, paramedics responded to a *574 call by Carolyn Ebel, the girlfriend of Her-sehel “Lobo” Bowser, who lived in an apartment on Artesia Boulevard in Los Angeles. They found Bowser lying unconscious on the floor, his head bleeding severely. A hammer was within a foot of the body near a pool of blood. Bowser died at the hospital later that day, having suffered twelve blunt injuries to the head and a fractured skull. The blows were consistent with force applied by the hammer. No fingerprints, blood, or DNA were found at the scene except for one print taken from a tool box, which matched the prints of the victim.

Ebel had left a wallet containing over $100 and the changer from her catering truck in a money bag at Bowser’s apartment and testified that Bowser, who was a drug dealer, kept a large amount of cash in the apartment. She saw Bowser in bed asleep about 9:30 in the morning when she went to pick up a paycheck; around noon, she got a call from Tracy Crisp, who lived in the building, saying that Crisp had been unable to reach Bowser on the telephone. As a result of that call, Ebel returned to Bowser’s apartment around 2:30 p.m.; the top lock was unlocked and when she opened the door as far as she could (Bow-ser was on the floor with his legs by the door), she saw that the living room was in shambles. Empty bags were strewn all over, and her wallet as well as the money bag with $40-70 and rolled change was gone. Ebel testified that Bowser kept his cocaine in a butter dish in a cupboard next to the stove in .the kitchen, which is- where he would take customers to negotiate sales. He stored the cocaine in ziploc plastic bags — two of powdered cocaine and one of rock cocaine — and one of the bags was marked with black “X’s.” Ebel noticed when she went into the kitchen after the crime that the cover of the butter container was off and the three bags of cocaine -that had been in it were gone.

Horton was a customer of Bowser’s whom Ebel had seen at Bowser’s apartment. . In October 1982, Horton lived at the Shangri Lodge, which was managed by Willie Dorn. Michael Graham also lived there, and he and Horton did odd jobs for Dorn. One day in October Horton asked Graham for a hammer that belonged to Dorn, which Graham gave him. Graham could not identify the hammer found near Bowser, but Dorn did. He testified that he had owned this hammer for twelve years, that Graham had been using it in October, and that he hadn’t seen it for about a week before October 10. At least one of the paint specks on the hammer was similar to the paint used on the Shangri Lodge buildings.

On the morning of October 10, Horton told Dorn that there was something he had to do and, if it worked out, Horton would be moving out the next day. The next day, around 9 o’clock, Dorn saw Horton leave in his car with James (“Doonie”) Cunnigan and Anthony Wilson. A few days later, Horton telephoned Dorn and asked if the police had been looking for him. He called back with the question several more times. Horton told Dorn to tell Graham that if anybody asked Graham whether he had given Horton anything to, tell them “no.”

Donald “Foo” McLaurin was the prosecution’s principal witness. The following is taken from his testimony. McLaurin had known- Horton since 1979 or 1980. They used drugs together. Horton had taken McLaurin to Bowser’s apartment building to buy cocaine, but McLaurin testified that he never went inside. Horton told McLau-rin that he bought the cocaine from someone named “Lo” or something like it. Bowser’s nickname was “Lobo.”

McLaurin testified that he, Horton, Wilson, and Horton’s brother William went to *575 Bowser’s building on the morning of October 10 and that Horton came out with a bag of cocaine. They went to Ray’s Motel where they proceeded to get high, then went to the Shangri Lodge where they were joined by Cunnigan and consumed more cocaine. According to McLaurin, Horton began to discuss a plan to rob his dealer, said that he could use a pipe to “slug him a few times,” and indicated he knew his dealer kept cocaine in one of the kitchen cabinets. McLaurin agreed to drive Horton to the dealer’s apartment, but instead left with his girlfriend.

About 1 p.m. on the 11th, Horton called McLaurin at work and asked McLaurin to meet him at Ráy’s Motel. Horton stated that he “did the number he was talking about last night.” Horton, Doonie, and Anthony were at Ray’s when McLaurin got there. McLaurin saw three bags of cocaine, two with a powdered substance and one with cocaine rocks. There were black “X’s” on one of the bags. McLaurin also saw a large roll of money. They began to smoke cocaine.

According to McLaurin, Horton said that he (Horton), Doonie, and Anthony went to the apartments on Artesia. Cun-nigan stated that “everything went down pretty smooth.” Horton said that he walked into the apartment, the dealer turned his back and closed the door, and Horton clubbed him on the head with a hammer. Horton then went to the kitchen cabinet and grabbed the cocaine. On the way back, Horton’s car overheated on the freeway and they left it. At Ray’s, Horton asked McLaurin to pick it up. McLaurin and Cunnigan returned to the car and retrieved a gym bag and a couple of bags of marijuana, but left the car. After McLaurin and Cunnigan returned, the group consumed more drugs and then McLaurin drove Horton, Doonie, and Anthony to the Greyhound bus depot.

McLaurin’s supervisor testified that McLaurin arrived for work on October 11 at 5:45 a.m. and left at 1 p.m. after receiving a telephone call. Much later, in November 1984, McLaurin was incarcerated on a probation violation and was housed in the same module as Horton. He met with Horton’s counsel.

At trial, McLaurin testified that he was in jail for a probation violation based on testing positive for cocaine, that he lied to Horton’s attorney when he talked with him because he feared harm if other inmates knew he was a “snitch,” and that neither the police nor the district attorney “helped him out” with the sentencing on the probation violation. McLaurin also admitted that he told defense counsel that he had been untruthful about everything he had told the police. He stated that he habitually smoked marijuana, had tried PCP, and had smoked a lot of cocaine the night before the murder; that he wasn’t functioning too clearly when the plan was being discussed; and that he was never charged with a crime even though he had driven Horton to the bus depot.

On April 1, 1985 a jury found Horton guilty of first degree murder and robbery, CahPenal Code §§ 187 and 211, finding true the special circumstance that the murder was committed during a robbery, CahPenal Code § 190.2(a)(17). In a bifurcated proceeding the jury also found true a special circumstance that Horton had a prior murder conviction. CahPenal Code § 190.2(a)(2). Following a penalty phase, the jury returned a verdict of death on April 16, 1985. On December 11, 1995 the California Supreme Court reversed the prior murder special circumstance and the death penalty verdict, but otherwise affirmed the judgment. People v. Horton, 11 Cal.4th 1068 , 47 Cal.Rptr.2d 516 , 906 P.2d 478 (1995). The state elected not to retry the penalty phase, therefore Hor *576 ton’s sentence stands at life in prison without the possibility of parole.

On October 17, 1989 Horton filed a petition for writ of habeas corpus in the California Supreme Court based on his trial by a commissioner instead of a superior court judge, which the court denied on August 12, 1991. In re Horton, 54 Cal.3d 82 , 284 Cal.Rptr. 305 , 813 P.2d 1335 (1991). He filed a second petition for writ of habeas corpus in the California Supreme Court on April 3, 1995, which the court denied on July 18,1996.

On October 2, 1997 Horton filed his first federal petition; he filed a Second Amended Petition on March 6, 2001. The district court denied all of Horton’s claims on the merits. The court granted a Certificate of Appealability (COA) on four issues that Horton pursues on appeal, and he has requested certification on five additional claims.

II

We review de novo a district court’s decision to grant of deny a 28 U.S.C. § 2254 habeas petition. Benn v. Lambert, 283 F.3d 1040, 1051 (9th Cir.2002). Because Horton’s petition was filed after April 24, 1996, the amendments to § 2254 under the Antiterrorism and Effective Death Penalty Act- (AEDPA) apply. Id. Under AEDPA, Horton is not eligible for habeas relief unless the decision of the California Supreme Court was “contrary to, or involved an unreasonable application’ of, clearly established Federal law, as determined by the Supreme Court of the United States,” or was “based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C-. § 2254(d); see also Benn, 283 F.3d at 1051 . A state court decision is contrary to clearly established federal law if the state court applies a rule that contradicts the-governing law set forth in Supreme Court cases or if the state court confronts a set of facts that are materially indistinguishable from a decision of the Supreme Court and nevertheless arrives at a result different from the Supreme Court precedent. Lockyer v. Andrade, 538 U.S. 63, 73 , 123 S.Ct. 1166 , 155 L.Ed.2d-144 (2003). A state court decision involves an unreasonable application of clearly established federal law if the state court identifies the correct governing legal principle from the United States Supreme Court’s decisions but unreasonably applies that principle to the facts of the prisoner’s case; the state court decision must be more than incorrect or erroneous, it must be objectively unreasonable. Id. at 75 , 123 S.Ct. 1166 . If a state law issue must be decided in order to decide a federal habeas claim, the state’s construction of its own law is binding on the federal court. Mullaney v. Wilbur, 421 U.S. 684, 691 , 95 S.Ct. 1881 , 44 L.Ed.2d 508 (1975).

Ill

Horton contends that trial counsel was ineffective in failing to impeach McLaurin with prior felony convictions, including a conviction on August 10, 1982 for possession of PCP with intent to sell. The California Supreme Court rejected this claim for lack of prejudice given McLaurin’s own testimony that revealed his extensive drug use and the fact that he was on probation -for a criminal conviction. We agree with the district court that this is not an unreasonable application of United States Supreme Court law as set out in Strickland v. Washington, 466 U.S. 668, 687 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984) (defendant must show both that counsel’s performance was deficient and that the deficient performance prejudiced the defense). The jury knew that McLaurin had used cocaine, marijuana and PCP, that he had a criminal history, and that he was an *577 admitted liar. In short, McLaurin’s credibility was so undermined anyway that evidence that he also had a conviction for possession with intent to sell PCP would not have affected the outcome.

IV

Horton also challenges his trial counsel’s performance on the ground that counsel advised him not to testify based on the mistaken belief that Horton’s prior murder conviction could be used to impeach him even though the trial judge had ruled that it was inadmissible. We agree with the district court’s bottom line, that the Strickland standard has not been met. Counsel’s declaration does not indicate when he told Horton that his prior conviction might be used to impeach him (it could have been before the trial judge’s ruling). 1 Nor is there any indication from Horton that he wanted to testify or would have testified; he gave no such signal at trial, see, e.g., Dows v. Wood, 211 F.3d 480, 487 (9th Cir.2000); United States v. Edwards, 897 F.2d 445, 446 (9th Cir.1990), or in the district court. Further, there is no submission indicating what he might have testified to. In these circumstances, and in light of Horton’s own inculpatory conduct and statements, it would be sheer speculation to say that the outcome would have been different.

V .

Horton maintains that his constitutional right to a fair trial was violated because his trial was conducted by a court commissioner who lacked jurisdiction. In California, the jurisdiction of a court commissioner derives from the parties’ stipulation. Cal. Const., art. VI, § 21. There was no formal stipulation to the commissioner’s serving in this case, but Horton and his counsel knew that the presiding judicial officer was a commissioner rather than a superior court judge. Knowing this, they appeared and allowed the pro-céedings to go forward without objection. As the California Supreme Court explained, a valid stipulation for purposes of California’s constitutional provision may arise as a result of the conduct of the parties. In re Horton, 284 Cal.Rptr. 305 , 813 P.2d at 1339 . This is known as the “tantamount stipulation doctrine,” and the attorney’s conduct alone is sufficient to trigger it. Id. at 1340., Here, the supreme court found that the conduct of Horton’s counsel was dispositive, and that Horton’s explicit authority or waiver was not required. It also concluded that trial by a commissioner did not offend Horton’s federal constitutional rights because the commissioner “takes on the mantle of a regularly appointed superior court judge in presiding over the trial and applies all the usual rules and procedures applicable in such a proceeding.” Id. at 1346.

We cannot say that the California Supreme Court’s determination is contrary to clearly established federal law. Under California law, the commissioner who presided over Horton’s trial had jurisdiction under the tantamount stipulation doctrine. Nothing' more is required by the cases upon which Horton relies, Gomez v. United States, 490 U.S. 858 , 109 S.Ct. 2237 , 104 L.Ed.2d 923 (1989) and English v. United States, 42 F.3d 473 (9th Cir.1994). Both recognize that the right to be tried by a person with jurisdiction is a critical element of the federal constitutional right to a fair trial, but that right was honored here. And as the district court held, to *578 the extent Article III jurisprudence or federal law interpreting the Federal Magistrates Act, 28 U.S.C. § 636 (b)(3), is relevant, Horton’s case falls between Gomez and Peretz v. United States, 501 U.S. 923, 936 , 111 S.Ct. 2661 , 115 L.Ed.2d 808 (1991) (finding no constitutional infirmity in the delegation of felony trial jury selection to a magistrate judge when petitioner’s counsel affirmatively welcomed the magistrate’s role rather than objecting).

VI

Horton’s motion to broaden the Certificate of Appealability is denied. Reasonable jurists would not find the district court’s assessment of the claims that he wishes to pursue debatable or wrong. Slack v. McDaniel, 529 U.S. 473, 484 , 120 S.Ct. 1595 , 146 L.Ed.2d 542 (2000). 2

VII

Horton alleges that the prosecution violated his rights under Brady v. Maryland, 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963), by failing to disclose a deal between the police and McLaurin, under which McLaurin agreed to testify as the prosecution’s star witness in exchange for immunity for anything he did on the weekend of the murder. The district court denied relief on this claim without making a factual finding as to the existence of a deal between the police and McLaurin. Instead, the court concluded that even assuming the alleged deal existed, evidence of the deal was not material under Brady v. Maryland. We disagree. 3 We hold that the prosecution’s failure to disclose the deal between the police and McLaurin violated Brady . Thus, we vacate the district court’s denial of Horton’s Brady claim and remand to the district court for further proceedings.

In criminal cases, the prosecution has a duty to disclose all material evidence that is favorable to the accused. Brady, 373 U.S. at 87 , 83 S.Ct. 1194 . This duty extends not only to exculpatory evidence but also to “evidence that the defense might have used to impeach the Government’s witnesses by showing bias or interest.” United States v. Bagley, 473 U.S. 667, 676 , 105 S.Ct. 3375 , 87 L.Ed.2d 481 (1985). Evidence is material if “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Id. at 682 , 105 S.Ct. 3375 . To prove materiality, a defendant need not demonstrate that it is more likely than not that he would have received a different verdict with the evidence; rather, “[a] ‘reasonable probability’ of a different result is ... shown when the government’s evidentiary suppression ‘undermines confidence in the outcome of the trial.’ ” Kyles v. Whitley, 514 U.S. 419, 434 , 115 S.Ct. 1555 , 131 L.Ed.2d 490 (1995) (quoting Bagley, 473 U.S. at 678 , 105 S.Ct. 3375 ).

We conclude that the state’s failure to disclose McLaurin’s leniency deal undermines confidence in the outcome of the trial for two reasons. First, McLaurin’s testimony was central to the prosecu *579 tion’s case. See Kyles, 514 U.S. at 444 , 115 S.Ct. 1555 (finding that non-disclosed evidence tending to undermine the reliability of key witness testimony was material); Giglio v. United States, 405 U.S. 150, 154-55 , 92 S.Ct. 763 , 31 L.Ed.2d 104 (1972) (finding that undisclosed deal with key prosecution witness was material non-disclosure); see also Banks v. Dretke, 540 U.S. 668, 699-703 , 124 S.Ct. 1256 , 157 L.Ed.2d 1166 (2004) (finding that non-disclosure of paid-informant status of key prosecution witness was material). Second, the deal would have provided powerful and unique impeachment evidence demonstrating that McLaurin had an interest in fabricating his testimony. See Napue v. Illinois, 360 U.S. 264, 270 , 79 S.Ct. 1173 , 3 L.Ed.2d 1217 (1959) (holding that some evidence of bias did not diminish value of other evidence of bias); Banks, 540 U.S. at 702-03 , 124 S.Ct. 1256 (finding that impeachment evidence was not “merely cumulative” where the withheld evidence was of a different character). We therefore hold that the California Supreme Court’s summary dismissal of Horton’s Brady claim was an unreasonable application of clearly established federal law as determined by the United States Supreme Court in Brady and related cases.

McLaurin’s testimony was the glue that held the prosecution’s case together. It was McLaurin’s testimony that described the plot and the motive to attack and kill Bowser. It was McLaurin’s testimony that linked Horton to the drugs and money that belonged to Bowser shortly after the murder. And most importantly, it was McLaurin’s testimony that revealed that Horton confessed to the crime. As the Supreme Court has noted, “A confession is like no other evidence. Indeed, ‘the defendant’s own confession is probably the most probative and damaging evidence that can be admitted against him.’ ” Arizona v. Fulminante, 499 U.S. 279, 296 , 111 S.Ct. 1246 , 113 L.Ed.2d 302 (1991) (quoting Bruton v. United States, 391 U.S. 123, 139 , 88 S.Ct. 1620 , 20 L.Ed.2d 476 (1968) (White, J., dissenting)).

As the prosecutor emphasized to the jury, McLaurin provided the only “direct” evidence that connected Horton to the crime. Indeed, without McLaurin’s testimony, the prosecution’s case was entirely circumstantial. No fingerprints, DNA evidence, or eyewitness testimony placed Horton at the scene. See Hayes v. Brown, 399 F.3d 972, 985, 988 (9th Cir.2005) (en banc) (holding that evidence of an undisclosed deal with a witness was material where the witness’s testimony regarding the defendant’s confession was undoubtedly the centerpiece of the prosecution’s case and almost all of the other evidence against the defendant was circumstantial).

The Supreme Court observed in Kyles that “[t]he likely damage [of suppressed evidence] is best understood, by taking the word of the prosecutor.... ” 514 U.S. at 444 , 115 S.Ct., 1555 . Here, the prosecutor stated in closing argument that it is “obvious to everybody in this courtroom that [MeLaurin’s] testimony in this case is very important” and urged three times that the jury ask to have it read back if they had “some doubt or question as to what he testified to.” The jury did in fact ask to have McLaurin’s testimony read back. See Gantt v. Roe, 389 F.3d 908, 915-16 (9th Cir.2004) (stating that “[w]e also know that the jury thought carefully about the matchbook because it submitted a question about it,” in concluding that suppressed evidence relating to the matchbook was material).

Further, in discussing the call that Horton allegedly made to McLaurin after the murder, the prosecutor stated, “If they didn’t call McLaurin, would this case- be solved? I don’t think anybody would know *580 anything about the case if it weren’t for the fact that the car broke down and they had to go from Ray’s Motel to the Greyhound bus depot.” 4 The prosecutor also argued that despite his drug use, McLau-rin was a credible, valuable witness.

The prosecutor’s emphasis on the importance of McLaurin’s testimony bolsters the conclusion that disclosure of the deal may have significantly damaged the prosecution’s case. See Hayes, 399 F.3d at 986 (“The importance of James’s testimony was underscored by the prosecution in its closing argument.”); Gantt, 389 F.3d at 915 (noting that the prosecutor “spent a good part of his summation arguing the importance of the matchbook”); cf. Stickler v. Greene, 527 U.S. 263, 295 , 119 S.Ct. 1936 , 144 L.Ed.2d 286 (1999) (holding that suppressed impeachment evidence was not material where the witness’s testimony “was not relied upon by the prosecution at all during its closing argument at the penalty phase”).

Although certain details of McLaurin’s account were corroborated by other witnesses, the most damning part of McLau-rin’s testimony — Horton’s confession — was not. Thus, evidence that would have impeached McLaurin’s credibility might well have altered the outcome of the trial. See Banks, 540 U.S. at 701 , 124 S.Ct. 1256 (holding that suppressed evidence of a witness’s role as an informant was material where his testimony was the “centerpiece” of the prosecution’s case and noting that had the evidence been disclosed, the jury “might well have distrusted [the informant’s] testimony, and, insofar as it was uncorroborated, disregarded it”); see also Silva v. Woodford, 279 F.3d 825, 854-55 (9th Cir.2002) (holding that an evidentiary hearing was warranted on a Brady claim involving a deal with a witness whose “credibility was a critical issue, given that he was the only witness who could identify [defendant] as the trigger man”).

It is true that McLaurin’s testimony was already severely impeached by his own admission that he habitually used drugs, lied to the police, and drove Horton to the bus depot after the killing. However, that the jury had other reasons to disbelieve McLaurin does not render the suppressed evidence of the deal immaterial. Evidence that the prosecution promised immunity to induce McLaurin to testify as its star witness is a wholly different kind of impeachment evidence, from which the jury reasonably could have inferred that McLaurin had an interest in fabricating his testimony. In Hayes , we held that disclosure of a deal with the prosecution’s key witness would not have been “merely cumulative impeachment” evidence, even though the witness was already subject to impeachment on the basis of transactional immunity, drug addiction, and his criminal record. 399 F.3d at 987 . Rather, we concluded that the additional disclosure “would have demonstrated that the State was going to great lengths to give [the witness] a powerful incentive to testify favorably, to the point of letting him go free on unrelated felony charges.” Id.; see also Banks, 540 U.S. at 702 , 124 S.Ct. 1256 (rejecting the government’s argument that suppressed evidence of a witness’s role as an informant was immaterial merely because the witness’s testimony was already impeached on grounds that were not “directly relevant” to his informant status); Napue, 360 U.S. at 270 , 79 S.Ct. 1173 (“[W]e do not believe that the fact that the jury was *581 apprised of other grounds for believing that the witness ... may have had an interest in testifying against petitioner turned what was otherwise a tainted trial into a fair one.”).

Moreover, as this court explained in Benn v. Lambert, where a witness is central to the prosecution’s case, the defendant’s conviction demonstrates that the impeachment evidence presented at trial likely did not suffice to convince the jury that the witness lacked credibility. 283 F.3d 1040, 1054 (9th Cir.2002). 5 In such cases, we noted, the suppressed impeachment evidence “takes on an even greater importance.” Id. In Benn , we ultimately held that:

Id. at 1056 . Because McLaurin’s testimony was critical to the prosecution’s case, we conclude that it is reasonably probable that the result of the trial would have been different had evidence of the deal been disclosed.

In sum, we hold that the prosecution’s failure to disclose the deal between McLaurin and the police violated Brady . The rule in this situation is clear and specific: the prosecution must disclose material evidence favorable to the defense. Brady, 373 U.S. at 87 , 83 S.Ct. 1194 . By implicitly finding that the suppression of McLaurin’s leniency deal was immaterial, the state court unreasonably applied Supreme Court:established federal law set down in Napue, Brady, Giglio, and Kyles . The recurrent theme of these cases is that where the prosecution fails to disclose evidence such as the existence of a leniency deal or promise that would be valuable in impeaching a witness whose testimony is central to the prosecution’s case, it violates the due process rights of the accused and undermines confidence in the outcome of the trial. Napue, 360 U.S. at 270 , 79 S.Ct. 1173 ; Giglio, 405 U.S. at 154 , 92 S.Ct. 763 ; Kyles, 514 U.S. at 444 , 115 S.Ct. 1555 . Here, the prosecution failed to disclose a promise of immunity given to McLaurin, its “star witness,” in exchange for his testimony, testimony that provided the only evidence of a motive and the opportunity to kill the victim and that included a confession by. Horton himself. The state court was not only wrong in its application of these cases, it was objectively unreasonable. See, 28 U.S.C. § 2254 (d)(1); Lockyer v. Andrade, 538 U.S. 63, 75-76 , 123 S.Ct. 1166 , 155 L.Ed.2d 144 (2003); see also Gantt, 389 F.3d at 916 (holding that the state court’s conclusion that the suppression of evidence did not violate Brady was an unreasonable application of clearly established federal law).

We therefore vacate the district court’s denial of Horton’s Brady claim and remand to the district court for a determination whether the state disputes the existence of the deal between McLaurin and the police. See Gantt, 389 F.3d at 916 . If the state does dispute the deal’s existence, the district court shall hold an evidentiary *582 hearing to resolve this dispute. 6 If the state concedes, or if the district court finds after an evidentiary hearing, that the deal existed, the district court shall grant a writ of habeas corpus ordering that Horton be released unless the state retries him within a reasonable time to be set by the district court. See id.

AFFIRMED IN PART, REVERSED AND REMANDED IN PART.

. We note that the declaration reflects a strategic concern about Horton's-taking the stand in the guilt phase with the penalty phase, including the special circumstance prior murder conviction that had not yet been stricken.

. Although we agree with the district court's conclusion on Horton’s appellate delay claim, we do so on the ground that he fails to make a substantial showing of the denial of a constitutional right under clearly established Supreme Court law.

. In addressing Horton's Brady claim, we assume, as the district court did, that the deal between the police and McLaurin existed as Horton has alleged. However, as discussed below, because no court has determined whether the deal existed, we remand to the district court for a resolution of this potential factual dispute.

. The dissent references pieces of evidence that are consistent with, or at least not inconsistent with, McLaurin's testimony; but as the prosecutor essentially conceded, without McLaurin’s testimony there would have been no case. This is precisely why his secret deal undermines confidence in the verdict.

. Although Supreme Court holdings are the only definitive source of clearly established federal law for purposes of the AEDPA, we may rely on circuit precedent as persuasive authority for determining whether a state court decision unreasonably applies Supreme Court law. Clark v. Murphy, 331 F.3d 1062, 1069 (9th Cir.), cert. denied, 540 U.S. 968 , 124 S.Ct. 446 , 157 L.Ed.2d 313 (2003).

. Although Horton's habeas petition is governed by the AEDPA, which limits a district court’s discretion to conduct evidentiary hearings, see 28 U.S.C. § 2254 (e)(2) (providing that petitioners who failed to develop the facts in state court may not obtain an evidentiary hearing in district court except in limited circumstances), here we assess the availability of an evidentiary hearing under pre-AEDPA law because Horton exercised sufficient diligence in seeking to develop the factual basis of his claim in the state court proceedings. See Williams v. Taylor, 529 U.S. 420, 437 , 120 S.Ct. 1479 , 146 L.Ed.2d 435 (2000) (“If there has been no lack of diligence at the relevant stages of the state court proceedings, the prisoner has not 'failed to develop’ the facts under § 2254(e)(2)'s opening clause, and he will be excused from showing compliance with the balance of the subsection's requirements.”).

Ordinarily diligence requires that a petitioner seek an evidentiary hearing in state court in the manner prescribed by state law. Id. Under California law, an appellate court, when presented with a state habeas petition, determines whether an evidentiary hearing is warranted only after the parties file formal pleadings, if they are ordered to do so. See People v. Duvall, 9 Cal.4th 464 , 37 Cal.Rptr.2d 259 , 886 P.2d 1252, 1258-61 (1995); People v. Romero, 8 Cal.4th 728 , 35 Cal. Rptr.2d 270 , 883 P.2d 388, 391-94 (1994). Here, the California Supreme Court summarily denied Horton's state habeas petition without ordering formal pleadings. Because Horton never reached the stage of the proceedings at which an evidentiary hearing should be requested, he has not shown "a lack of diligence at the relevant stages of the state court proceedings” and therefore is not subject to AEDPA’s restrictions on evidentiary hearings.

Under pre-AEDPA law, a habeas petitioner is entitled to an evidentiary hearing on a claim where the facts are in dispute if (1) he has alleged facts that, if proven, would entitle him to relief, and (2) he did not receive a full and fair evidentiary hearing in state court. See Silva, 279 F.3d at 853 . Because, as noted, Horton would be entitled to relief if his allegation of the deal were proven, and because Horton was not afforded an evidentiary hearing in state court, Horton is entitled to an evidentiary hearing on his Brady claim if the state disputes that the deal existed. See id. at 855.