Valerio v. Crawford, 306 F.3d 742, 764 (9th Cir.2002) (en banc), cert. denied, — U.S. -, 123 S.Ct. 1788 , 155 L.Ed.2d 695 (2003), overruled the portion of United States v. Zuno-Arce, 209 F.3d 1095, 1100-01 (9th Cir.2000), amended (to include partial dissent) by 245 F.3d 1108 (9th Cir.2001), that applied Circuit Rule 22-1(d). In accordance with Valerio , we now must consider the appellate briefing in Zuno-Arce as a request to expand the certificate of appealability (“COA”) issued by the district court. We deny a COA as to the Mooney-Napue claim, the ineffective assistance of counsel claim, and the double jeopardy claim. We grant a COA as to the Brady-Bagley claim, but affirm on the merits because the undisclosed evidence is not material within the meaning of that doctrine.

FACTUAL AND PROCEDURAL HISTORY

A factual and procedural history is contained in our earlier opinion. 209 F.3d at 1096-99 . We incorporate that material by reference. The district court’s opinion is published, and also includes a thorough factual discussion at United States v. Zuno-Arce, 25 F.Supp.2d 1087 (C.D.Cal.1998).

STANDARDS OF REVIEW

A. General Standards

We review de novo a district court’s denial of a § 2255 motion. United States v. McMullen, 98 F.3d 1155, 1156 (9th Cir.1996). We review for clear error a district court’s factual findings that underlie the disposition of a § 2255 motion. Sanchez v. United States, 50 F.3d 1448, 1452 (9th Cir.1995).

B. Standard for Issuing a COA

A COA may issue only upon the “substantial showing of the denial of a constitutional right.” 28 U.S.C. § 2253 (c)(2).

Slack v. McDaniel, 529 U.S. 473, 484 , 120 S.Ct. 1595 , 146 L.Ed.2d 542 (2000). The Supreme Court recently elaborated on what is required to make such a showing:

Miller-El v. Cockrell, 537 U.S. 322 , 123 S.Ct. 1029, 1039 , 154 L.Ed.2d 931 (2003).

DISCUSSION

A. The Mooney-Napue Claim

In our 2000 opinion in Zuno-Arce, we recognized that § 2255 requires an eviden-tiary hearing unless the “motion and the files and records of the case conclusively show that the prisoner is entitled to no relief.” 28 U.S.C. § 2255 ; Zuno-Arce, 209 F.3d at 1102 . Applying that standard, we held that the district court did not err in denying an evidentiary hearing based on the material that it considered timely. Id. at 1103 . However, we went further. Re-framing the district court’s question regarding timeliness, we held that Zuno-Arce was not entitled to an evidentiary hearing even considering all the evidence offered in support of his Mooney-Napue claim. Id. Because of the breadth of the standard set out in § 2255, we necessarily concluded that the motion and the files and records of the case conclusively showed that Zuno-Arce was entitled to no relief on his Mooney-Napue claim. We continue to stand by that holding.

To prevail on a claim based on Mooney-Napue, the petitioner must show that (1) the testimony (or evidence) was actually false, (2) the prosecution knew or should have known that the testimony was actually false, and (3) that the false testimony was material. See Napue, 360 U.S. at 269-71, 79 S.Ct. 1173 . The first requirement is missing here. Zuno-Arce’s evidence failed to demonstrate that the testimony of Lopez or Godoy was false.

The proffered evidence was primarily that Cervantes’ recantation demonstrated that Lopez and Godoy testified falsely. However, the district court found that Cervantes’ recantation was unreliable. As we recognized in another context, that finding is not clearly erroneous. United States v. Matta-Ballesteros, 213 F.3d 644 , 2000 WL 297328 , at *1 (9th Cir. Mar. 21, 2000) (unpublished decision). Cervantes changed his story back and forth several times, before finally testifying that the story he had told during Zuno-Arce’s first trial was the truth. Considering Cervantes’ history of self-interested recantations, the district court did not clearly err in determining that the recantation was, at best, unreliable. Further, Cervantes’ recantation, even if true, does not demonstrate anything about the truth or falsity of Lopez’ and Godoy’s testimony.

Zuno-Arce also relies on impeachment evidence that would have undermined the credibility of Lopez and Godoy. None of it, however, was sufficient to establish that their testimony was false. The evidence shows that Lopez and Godoy were criminals and that the government had promised them money in exchange for their testimony. Those facts, without more, do not demonstrate falsity. In the circumstances, we decline to issue a COA on this claim.

B. The Brady-Bagley Claim

We apply the same assumptions regarding the timeliness of Zuno-Arce’s claimed new evidence here as we did to his Mooney-Napue claim. We need not decide the timeliness question, because Zuno-Arce is not entitled to relief even if all the evidence is considered. See Zuno-Arce, 209 F.3d at 1103 .

As this court recently summarized Brady-Bagley law:

United States v. Ciccone, 219 F.3d 1078, 1085 (9th Cir.2000) (citations altered).

The new evidence supporting Zuno-Arce’s Brady-Bagley claim falls into two basic categories: (1) evidence arising out of Cervantes’ allegedly false testimony at the first trial and (2) impeachment evidence concerning Lopez and Godoy. Even assuming that this evidence is both favorable and undisclosed, Zuno-Arce cannot show prejudice, because there is no reasonable probability that, had it been disclosed, the evidence would have made a difference to the outcome of the trial.

1. Cervantes’ Recantation

To prevail, Zuno-Arce must show that, sometime before or during his second trial, the government knew that Cervantes had testified falsely in the first trial. As noted above, however, Zuno-Arce has failed to demonstrate that Cervantes testified falsely, so a fortiori there is no way that Zuno-Arce could have demonstrated that the government knew that Cervantes testified falsely. See Matta-Ballesteros, 2000 WL 297328 , at *1 (holding that the district court did not clearly err in rejecting Cervantes’ recantation as unreliable).

Included in Cervantes’ recantation was a claim that he had received more money than the government had disclosed. Even if that claim were true, the defense knew during Zuno-Arce’s trials that Cervantes had been given substantial payments. In fact, the defense cross-examined Cervantes extensively about those payments at the first trial. Moreover, undisclosed payments to Cervantes could not have made a difference in the second trial, because Cervantes did not testify.

2. Impeachment Evidence About Lopez and Godoy

Zuno-Arce cites numerous pieces of allegedly undisclosed evidence that, he argues, could have impeached Lopez and Godoy. That evidence is immaterial under Bagley because it could not have made any difference to the outcome of the trial. The defense presented hefty and devastating impeachment evidence at trial, concerning past crimes, government favors, and inconsistencies in testimony, but nonetheless the jury convicted on Lopez’ and Godoy’s testimony. See Zuno-Arce, 25 F.Supp.2d at 1106 (detailing impeachment evidence at trial). The additional evidence on which Zuno-Arce relies could not have altered that result.

(a) Government Payments

Zuno-Arce alleges that Lopez and Go-doy were promised lump-sum payments of $100,000 for their testimony. This allegation is not borne out by the record. Zuno-Arce presented no evidence that before or during trial the government had promised to pay off the monthly installments of $3,000 in a lump sum. The government presented affirmative evidence to the contrary — that the lump-sum arrangement was devised after trial to terminate the government’s ongoing obligations to numerous witnesses.

The government does not dispute that it paid Lopez and Godoy $100,000 each in late 1995 (three years after the trial). Even assuming that there was an undisclosed earlier promise to make lump-sum payments, the payments were made in satisfaction of the $3,000 monthly payments that Lopez and Godoy had been promised. The jury knew about those monthly payments, so a final satisfaction of the debt likely would have made no difference in the jury’s assessment of credibility.

(b) Government Assistance With Lopez’ Arrest for Spousal Abuse

Zuno-Arce offers evidence demonstrating that the government took measures to secure Lopez’ release after his 1992 arrest for spousal abuse, which was a deportable offense. In view of the impeachment evidence that the jury heard at trial, this evidence would have been unlikely to produce a different verdict.

During Zuno-Arce’s second trial, the jury learned that Lopez had participated in the kidnapping, torture, and murder of four Jehovah’s Witnesses and of an American couple. Zuno-Arce, 25 F.Supp.2d at 1106 . The jury also knew that, despite his violent and criminal character, the government was paying Lopez $3,000 a month and had given him immunity in the Ca-marena case and an INS work permit. It is safe to conclude that the jury already knew that Lopez was violent and criminal and that the government aided him in evading responsibility for his crimes and in immigration matters. If the jury was willing to believe Lopez the multiple-murderer, the jury surely would have been willing to believe Lopez the wife-batterer.

(c)Evidence Rebutting Details of Lopez’ and Godoy’s Testimony

The private investigator’s report included several examples of inconsistencies in Lopez’ and Godoy’s testimony. See id. at 1110-13 , 1118 n. 46. None of this evidence pertains directly to the evidence that Lopez and Godoy presented to demonstrate Zuno-Arce’s connection with the drug cartel. At most, the evidence adds up to an attack on Lopez’ and Godoy’s credibility— something that had been done effectively at trial without this evidence. In view of the extensive impeachment evidence that was offered, the allegations of additional, tangential inconsistencies could not have made a difference in the outcome.

(d)Berellez’ Recruiting Techniques

Zuno-Arce also cites evidence arising out of an arrest of Special Agent Berellez for drunk driving in December of 1991. Berellez’ supervisor wrote a letter stating that Berellez had been drinking during recruitment efforts for the Camarena investigation. Assuming that this evidence is favorable, it cannot be material because it could have made no difference. Only speculation ties Berellez to Lopez and Go-doy that night, so it is unclear what value the arrest would have in impeaching Lopez and Godoy.

(e)The Redacted DEA-6 Form for Ramon Lira

Informant Ramon Lira told the DEA about a November 1984 meeting he had witnessed. Lira stated that he had looked into a room at Fonseca’s house for 15 to 20 seconds, saw the President of Mexico, a past President of Mexico, and the Governor of Jalisco sitting around a table that had a stack of U.S. currency on it. According to Lira, he overheard the words “Búfalo” and “Camarena.” When the government provided the report of Lira’s interview, it redacted the section that dealt with that evidence.

The redacted material shows only that some members of the cartel may have known as early as November 1984 that Camarena was responsible for the raid on the marijuana fields at El Búfalo. That inference does not help Zuno-Arce because Lopez and Godoy testified that Zuno-Arce had attended meetings to divine the identity of the responsible party before November of 1984. Moreover, it is unlikely that Zuno-Arce would have called Lira as a witness, because Lira’s testimony was inculpatory. See id. at 1107-08 .

3. Conclusion

Considering the central role that Lopez and Godoy played in Zuno-Arce’s second trial, and considering the extent of the allegedly undisclosed evidence, we grant a COA as to this claim. See Carriger v. Stewart, 132 F.3d 463, 480 (9th Cir.1997) (en banc) (discussing the importance of undisclosed impeachment evidence targeting the government’s “star witness”). However, because Cervantes’ recantation was unreliable, and because substantial impeachment evidence presented at trial already discredited Lopez and Godoy in much more dramatic ways, we are unpersuaded by the Brady-Bagley claim on the merits.

C. Claims of Ineffective Assistance of Counsel and Double Jeopardy

The district court rejected these claims as untimely and as improperly presented. Zuno-Arce, 25 F.Supp.2d at 1095-96 . In the alternative, the court rejected both claims on the merits. Id. at 1096-97, 1113-15 . We assume, without deciding, that the district court should have reached the merits of these claims. We conclude nonetheless that Zuno-Arce has failed to meet the standard for granting a COA.

1. Ineffective Assistance

Zuno-Arce alleges that his counsel was ineffective for failing to discover the evidence supporting his Brady-Bagley claim sooner. His claim is unpersuasive. Assuming, without deciding, that Zuno-Arce had a right to counsel at the relevant time, and further assuming, without deciding, that his lawyer’s performance was objectively unreasonable, he cannot establish prejudice under the second prong of Strickland v. Washington, 466 U.S. 668, 687 , 104 S.Ct. 2052 , 80 L.Ed.2d 674 (1984). This conclusion follows from our holding, above, that there is no reasonable probability that the result of the trial would have been different even if more diligent counsel had discovered and presented the additional evidence on which Zuno-Arce now relies.

2. Double Jeopardy

Under ordinary double jeopardy principles, Zuno-Arce could be retried, because his conviction was set aside “because of some error in the proceedings leading to conviction,” not for lack of evidence. Lockhart v. Nelson, 488 U.S. 33, 38 , 109 S.Ct. 285 , 102 L.Ed.2d 265 (1988). Nevertheless, he seeks to invoke the double jeopardy bar to his retrial on the ground that the government knowingly presented Cervantes’ perjured testimony in his first trial.

“The Supreme Court has ... held that retrial is barred when the defendant moves for and is granted a mistrial on the basis of deliberate prosecutorial misconduct intended to provoke a mistrial motion by the defense.” Greyson v. Kellam, 937 F.2d 1409, 1413 (9th Cir.1991) (citing Oregon v. Kennedy, 456 U.S. 667, 679 , 102 S.Ct. 2083 , 72 L.Ed.2d 416 (1982)). Here, however, Zuno-Arce did not move for— much less receive — a mistrial on the basis of prosecutorial misconduct, so this exception does not apply.

More fundamentally, this argument is based on a faulty premise — that the government knowingly presented Cervantes’ perjured testimony at the first trial. For reasons already discussed, we have rejected that contention.

CONCLUSION

We deny a COA as to Zuno-Arce’s Mooney-Napue claim, his ineffective assistance of counsel claim, and his double jeopardy claim. We grant a COA on the Brady-Bagley claim, but we are unpersuaded by that claim on the merits.

AFFIRMED.

. Except to the extent that Valerio overruled our holding concerning the application of Circuit Rule 22-1 (d), we hereby reaffirm our previous opinion. . Mooney v. Holohan, 294 U.S. 103 , 55 S.Ct. 340 , 79 L.Ed. 791 (1935) (per curiam); Napue v. Illinois, 360 U.S. 264 , 79 S.Ct. 1173 , 3 L.Ed.2d 1217 (1959). .Brady v. Maryland, 373 U.S. 83 , 83 S.Ct. 1194 , 10 L.Ed.2d 215 (1963); United States v. Bagley, 473 U.S. 667 , 105 S.Ct. 3375 , 87 L.Ed.2d 481 (1985). . In Matta-Ballesteros , we held that the district court did not abuse its discretion in not granting .a new trial on the ground that Cervantes’ recantation was not credible. Satis faction of that lesser standard necessarily means that the district court did not clearly err. We cite Matta-Ballesteros pursuant to Circuit Rule 36-3(b)(i), which permits citation to unpublished dispositions when relevant under the doctrine of law of the case. Zuno-Arce and Matta-Ballesteros were co-defendants in the same trial. Both Zuno-Arce and Matta-Ballesteros based their claims before the district court on the contention that Cervantes had testified falsely. See United States v. Maybusher, 735 F.2d 366, 370 (9th Cir.1984) (discussing circumstances that would give rise to application of law of the case doctrine in the criminal context). . For the same reason, we need not address Zuno-Arce’s "actual innocence” claim. That claim is not in itself a constitutional claim, but would serve only to remove the timeliness bar so that claims may be heard on the merits. Majoy v. Roe, 296 F.3d 770 , 776 n. 1 (9th Cir.2002).