
572 F.3d 252 (2009)
Ragheed AKRAWI, Petitioner-Appellant,
v.
Raymond BOOKER, Respondent-Appellee.
No. 07-1984.
United States Court of Appeals, Sixth Circuit.
Argued: June 17, 2009.
Decided and Filed: July 10, 2009.
*254 ARGUED: Andrea Lynn Reino, Gerhardstein & Branch, Cincinnati, Ohio, for Appellant. Brian O. Neill, Office of the Michigan Attorney General, Lansing, Michigan, for Appellee. ON BRIEF: Richard L. Steinberg, Richard L. Steinberg, *255 P.C., Detroit, Michigan, for Appellant. William C. Campbell, Office of the Michigan Attorney General, Lansing, Michigan, for Appellee.
Before: GILMAN and McKEAGUE, Circuit Judges; GRAHAM, District Judge.[*]

OPINION
McKEAGUE, Circuit Judge.
This is an appeal from an order denying a petition for writ of habeas corpus. Petitioner contends that his 1991 drug-trafficking conviction is constitutionally infirm because the prosecution suppressed evidence favorable to him, in violation of its duties under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). For the reasons that follow, we affirm.

I. BACKGROUND

A. Trial Proceedings
In October 1991, Ragheed Akrawi was tried in Oakland County (Michigan) Circuit Court with one of eight other co-defendants, charged with conspiring to possess with intent to deliver in excess of 650 grams of cocaine. After the jury found Akrawi guilty as charged, he was sentenced to life imprisonment.[1] The prosecution's case was based in part on the testimony of Wissam Abood.[2] Abood had been arrested and detained in neighboring Macomb County in February 1990 in connection with a similar cocaine trafficking conspiracy charge. In May, Abood's bond was reduced so he could be released from jail to cooperate with ongoing law enforcement efforts, including the investigation and prosecution of Ragheed Akrawi. The bond reduction was instigated by Abood's attorney, Sheldon Halpern, who advised authorities that Abood might be able to help them out. Pursuant to an arrangement between the Macomb County Prosecuting Attorney and DEA Special Agent Sergeant Chuck Pappas of the Troy Police Department, who was supervising the Akrawi investigation, Pappas was to advise the prosecutor of the extent of Abood's cooperation while released on bond.
Abood subsequently testified in Akrawi's trial that on two occasions, on successive days in the Summer of 1988, at the same coffee shop, he purchased a quarter-kilo of cocaine from Akrawi for a friend. The purchase price for each transaction was $5,200. A week later, Abood made two more purchases of cocaine from Akrawi for the same friend: a one-ounce purchase for $500 and a two-ounce purchase for $1200. Abood testified that no one promised him anything for his testimony and no one had threatened him. On cross-examination, Akrawi's attorney, James Howarth, tested Abood's motivation for testifying. Abood admitted being concerned about the very serious charges pending against him in Macomb County and about the possibility that he, an Iraqi national, could be deported. *256 As to whether any deal might be worked out such that his cooperation could result in favorable treatment in Macomb County, Abood said he did not know what the outcome would be; that he was relying on his attorney, in whom he had confidence. Abood acknowledged having testified before the grand jury that his motive for testifying against Akrawi was "to help rid the streets of drugs," a reason apparently stemming from regrets about the prevalence of drugs in his community and the impact drugs had had on his family.[3]
Abood's testimony was corroborated by Special Agent Pappas, who testified that Abood was not promised anything. Pappas acknowledged having agreed, in Abood's counsel's presence, that he would report the extent of Abood's cooperation to Macomb County Prosecuting Attorney Carl Marlinga. He explained that this was a promise made to Marlinga, in connection with the bond-reduction, not to Abood or his attorney, Sheldon Halpern. Consistent with this promise, Pappas reported Abood's cooperation to Macomb County Assistant Prosecutor Michael Suhy, but denied having requested any charge-reduction or sentence-reduction. Any such decision, he explained, would have to be made by the prosecutor. From his conversations with Suhy, however, Pappas testified that he understood the Macomb County authorities were considering a charge-reduction for Abood.
Macomb County Assistant Prosecutor Trish Fresard also corroborated Abood's testimony. She was assigned to Abood's case when the bond-reduction was arranged. She acknowledged that Abood was then charged with a cocaine-trafficking offense that carried a mandatory penalty of life imprisonment without parole. She acknowledged that a charge-reduction was a possibility that Marlinga would consider, depending on the extent of the assistance afforded by Abood. Fresard denied ever making a promise that Abood would be granted a charge-reduction if he cooperated.
Assistant Prosecutor Suhy later assumed responsibility for the Abood case from Fresard. He acknowledged that, depending on the extent of Abood's cooperation with Oakland County authorities, a reduction of the charge against Abood was a possibility under consideration. However, consideration of any charge-reduction was premature from the perspective of the prosecuting attorney's office, because at the time Abood testified in the Akrawi trial, Halpern was still avidly pursuing outright dismissal of the charges against his client based on an entrapment defense.
Based on the foregoing summary of relevant trial testimony, the jury was presented with consistent evidence that there was no express agreement between Abood and the prosecution team regarding specific consideration for his cooperation. The jury certainly learned, however, that there was an implicit understanding that, depending on the nature and extent of Abood's assistance in connection with the Akrawi prosecution, the charge pending against him in Macomb County could be reduced.
Indeed, Akrawi's attorney emphasized this very point in his closing argument. He acknowledged that the jury could reasonably conclude that Abood did not have a firm deal, but he suggested they could also find it "crystal clear," based on the testimony of the prosecution team itself, that Abood was doing everything possible to win favor in Macomb County and avoid such consequences as deportation or life *257 imprisonment. Howarth challenged the jury to see that Abood's professed motive, to rid the streets of drugs, was "a major league lie." Rather, he argued, everybody knew that his real motive was to win favor in Macomb County.
Nonetheless, Akrawi was found guilty as charged. His conviction was affirmed by the Michigan Court of Appeals on October 24, 1995. The Michigan Supreme Court denied leave to appeal on November 22, 1996.

B. Post-Conviction Proceedings
In the meantime, Abood's situation had improved dramatically. On February 19, 1992, Halpern wrote to the Oakland County prosecutor who had handled Akrawi's trial, Lawrence Bunting, explaining that Suhy had now consented to reduce the charges against Abood, and soliciting a letter detailing the extent of Abood's assistance. Bunting responded with a letter explaining that Abood's testimony was "crucial" and that the prosecution would have been much different without it. On March 17, 1992, Abood entered into a plea agreement, pleading guilty to delivering less than 50 grams of cocaine. He was sentenced to lifetime probation on the recommendation of prosecutors Marlinga and Suhy.
On August 12, 1996, Abood executed an affidavit purporting to recant or correct his testimony in the Akrawi case. In it, he states that he falsely testified that he had no deal. However, he identifies "the deal" only in amorphous terms: "Chuck Pappas told me that he wanted my cooperation and if he got it, he could in turn help me with my situation."
Abood's attorney, Sheldon Halpern, also provided an affidavit, dated March 19, 1998, detailing his impressions of "the deal." He described it as an agreement with law enforcement for a substantial reduction of the charges pending against Abood. Halpern's affidavit also alludes to a letter he sent to prosecutor Fresard on May 14, 1990, purporting to memorialize the understanding. In relevant part, the letter provides:
I am writing to confirm the understanding under which your office has consented to the entry of an Order changing the Bonds herein to ten percent (10%) Bonds. In addition, I confirm herewith [sic] your office to reduce the over 650 grams case to over 225 grams, with further reductions of one (1) or more levels depending on the extent of assistance my client affords.
I believe this letter to be necessary as none of the discussions, including the consent to the change in Bonds, was placed on the record for the obvious reasons.
If your understanding differs in any manner than as stated herein, please contact me by return mail.
Halpern letter 5/14/90, JA 1525 (footnote omitted).[4]
Armed with these materials, Akrawi moved for relief from judgment in the Oakland County Circuit Court in September 1998. Akrawi contended that he was denied a fair trial due to the prosecution's failure to disclose information regarding its cooperation agreement with Abood and due to the prosecution's presentation of false testimony regarding the agreement. An evidentiary hearing was conducted on July 18 and 23, 2001. Abood refused to *258 testify, asserting his Fifth Amendment privilege against self-incrimination because he was not granted immunity. The court, Hon. Nanci J. Grant, received testimony from Halpern, Pappas, Fresard, Bunting, Suhy and Howarth before issuing an opinion and order on May 30, 2002, concluding that Akrawi was entitled to a new trial.
Halpern testified that Pappas had made assurances to him consistent with the terms memorialized in his letter to Fresard. Halpern understood this to comprise a "firm agreement," inasmuch as Fresard did not communicate any objection in response to the letter. Halpern further testified that some years after the Akrawi trial, Abood told him that prosecutor Bunting had advised Abood, before he testified in the Akrawi trial, that he had not been given any consideration for his testimony and he was expected to so testify.
Pappas remained true to his trial testimony, maintaining that he made no promises to Abood, although he agreed with the Macomb County authorities to report Abood's cooperation to them. Pappas testified that he lacked authority to make any promise of a charge-reduction. Fresard, too, testified that she had made no promise to Abood and lacked the authority to do so. Fresard denied ever having seen the May 14 letter from Halpern, although she did not dispute that it was found in her file. Fresard acknowledged that the possibility of a charge-reduction was the benefit that Abood hoped or expected to gain by his cooperation.
After summarizing the salient testimony, Judge Grant's opinion sets forth her reasoning in one paragraph:
In light of the foregoing, resolution of this motion turns exclusively on the factual dispute. The Court believes the evidence compels a finding in Defendant's favor. First and foremost, Attorney Halpern's confirming letter must be given great weight, as it describes in detail the consideration that Abood was to receive and, in fact, actually ended up receiving. Moreover, there can be no dispute that the letter was sent, as it was discovered in the Prosecutor's file. The allegations in the letter were further corroborated by the telephone message from Fresard and the testimony of James Howarth [reflecting Fresard's and Suhy's understanding that Abood had been given reason to expect favorable treatment in exchange for his cooperation]. In light of this evidence, the Court simply cannot imagine a plausible scenario under which these events would have occurred in the absence of Abood having received a charge reduction deal in exchange for his testimony against Defendant. Therefore, Defendant has established that his due process rights were violated, and is entitled to a new trial.
Order and Opinion 5/30/02, JA 1516-17. Judge Grant thus held that the prosecution's failure to disclose to Akrawi what it knew about its communications with Abood that may have induced him to testify was a failure to disclose material impeachment evidence, contrary to Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), and United States v. Bagley, 473 U.S. 667, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).
Before a new trial could be conducted, however, the Michigan Court of Appeals reversed the grant of relief from judgment on December 9, 2003. The court cited three reasons. First, the court held that Akrawi had failed to show good cause for his failure to raise this issue in his direct appeal, a prerequisite to relief from judgment under Mich. Ct. R. 6.508(D)(3). Second, the court held that Judge Grant clearly *259 erred in finding that Abood testified pursuant to an existing agreement or deal. The court of appeals construed the record as showing that no agreement was reached until after Abood testified. All earlier communications between law enforcement and Abood or Halpern were deemed to relate only to "a future possibility of leniency," something the prosecution was not required to disclose. Third, the court held Akrawi had failed to show actual prejudice stemming from the asserted nondisclosure:
When we consider all the foregoing circumstances and testimony, further disclosure of a possible deal would not have resulted in a different outcome at trial. As discussed, evidence was presented to the jury that Abood would potentially receive consideration for his testimony, and Abood was not the most significant witness testifying against defendant. The introduction of more details of Abood's future deal with the Macomb County Prosecutor would not have changed the outcome of defendant's trial.
Unpublished Opinion 12/9/03, JA 185. The Michigan Supreme Court denied leave to appeal on December 29, 2004 in a one-sentence order.

C. Habeas Petition
On November 29, 2005, Akrawi filed his petition for writ of habeas corpus in the Eastern District of Michigan, naming as respondent Raymond Booker, Warden of the Ryan Correctional Facility in Detroit. In relevant part, the petition asserts that petitioner was denied his constitutional right to a fair trial when the prosecution and crucial witness not only failed to disclose, but arbitrarily and deliberately acted in covin concert to conceal the fact that the witness was accorded a substantial deal in exchange for his highly suspect testimony. The district court denied the petition in an opinion and order dated June 30, 2007. The district court acknowledged the warden's statute-of-limitations and procedural-default defenses, but refrained from addressing them because they are not jurisdictional defenses. On the merits, the district court agreed with petitioner that the prosecution had wrongfully suppressed evidence favorable to Akrawi:
The record indicates that, although there was no formal deal between Wissam Abood or his attorney and Macomb County officials at the time of Petitioner's trial, there was at least an informal agreement to reduce the charges against him in return for his testimony against Petitioner and others. And because Abood and law enforcement officials denied the existence of a deal, it was unreasonable for the state appellate court to conclude that the prosecutor did not withhold favorable evidence from Petitioner.
Opinion and order 6/30/07, JA 1678.[5] However, the district court agreed with *260 the Michigan Court of Appeals that the prosecution's nondisclosure of the informal agreement did not result in such actual prejudice to Akrawi as to warrant habeas relief. The district court recognized that reasonable jurists could debate the resolution of this question of prejudice and so granted a certificate of appealability on this lone issue.
On appeal, Akrawi insists that the prosecution suppressed material exculpatory evidence and then compounded the wrong by concealing it through perjury, resulting in "structural error" mandating relief to restore the integrity and public reputation of the judicial proceedings.

II. ANALYSIS

A. Statute of Limitations
Warden Booker timely raised a statute-of-limitations defense in his response to the habeas petition. The Warden argued, and Akrawi has not disputed, that the habeas petition is governed by the one-year period of limitation established by the Anti-Terrorism and Effective Death Penalty Act ("AEDPA") at 28 U.S.C. § 2244(d). The Warden demonstrated that even though the running of the statute was tolled during the pendency of Akrawi's pursuit of post-conviction relief in the Michigan courts, the instant petition was not filed until 154 days after his one-year period had expired. The Warden has reiterated the defense on appeal.
In response, Akrawi has not challenged the Warden's time calculations, in the district court or on appeal. Nor has he attempted to invoke the doctrine of equitable tolling. See Keenan v. Bagley, 400 F.3d 417, 420 (6th Cir.2005) (petitioner bears the burden of showing entitlement to equitable tolling); Pace v. DiGuglielmo, 544 U.S. 408, 418, 125 S.Ct. 1807, 161 L.Ed.2d 669 (2005) (petitioner must establish "(1) that he has been pursuing his rights diligently, and (2) that some extraordinary circumstance stood in his way."). Nor has Akrawi attempted to avoid the time-bar through a showing of actual innocence. See Ross v. Berghuis, 417 F.3d 552, 555-56 (6th Cir.2005) (assuming the applicability of the actual-innocence equitable-tolling rule to a non-capital case, petitioner must demonstrate by presentation of new reliable evidence that he did not commit the acts for which he was convicted).
The district court addressed the merits of the petition without ruling on the statute of limitations defense, observing that the defense is not jurisdictional. Yet, though the defense is not jurisdictional, it has been timely asserted by the Warden, and per the restrictions on habeas relief prescribed by Congress in AEDPA, effectively bars relief absent a showing that the petition's untimeliness should be excused based on equitable tolling and actual innocence. McCray v. Vasbinder, 499 F.3d 568 (6th Cir.2007) (reversing order granting habeas relief because the "gateway requirements" for excusing a time-barred petitioni.e., equitable tolling and actual innocence-had not been satisfied); Connolly v. Howes, 304 Fed.Appx. 412 (6th Cir. 2008) (unpublished) (upholding dismissal of time-barred petition and observing that equitable tolling requires credible new evidence of actual innocence).
Petitioner Akrawi does not deny that his petition is untimely. Nor has he even attempted to carry his burden of showing entitlement to equitable tolling. It follows *261 that the petition should have been dismissed. Yet, for the reasons that follow, we conclude, like the district court, that even if the merits of the petition were considered, the result would be the same: Akrawi is not entitled to habeas relief.

B. Procedural Default
The Warden also timely asserted procedural default as a defense, in the district court and on appeal. Indeed, the Michigan Court of Appeals, as its first reason for reversing the grant of post-conviction relief, cited Akrawi's failure to show (1) good cause for his failure to assert this issue in his direct appeal, and (2) that the error resulted in actual prejudice, as required for relief under Mich. Ct. R. 6.508(D)(3). JA 183-84. The Michigan Supreme Court denied leave to appeal in a one-sentence order, stating simply "we are not persuaded that the question presented should be reviewed by this Court." People v. Akrawi, 471 Mich. 944, 690 N.W.2d 104 (Table) (2004).
Federal courts ordinarily "will not review a question of federal law decided by a state court if the decision of that court rests on a state law ground that is independent of the federal question and adequate to support the judgment." Howard v. Bouchard, 405 F.3d 459, 475 (6th Cir.2005) (quoting Coleman v. Thompson, 501 U.S. 722, 729, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991)). For purposes of procedural default, the federal court is concerned with the "last explained state court judgment." Id. at 475-76 (quoting Munson v. Kapture, 384 F.3d 310, 314 (6th Cir.2004)). Here, the Michigan Court of Appeals ruling is clearly the last explained state court judgment. It expressly relied at least in part on the unmet requirements of Mich. Ct. R. 6.508(D)(3) as a reason for denying post-conviction relief. It is well-established in this circuit that the procedural bar set forth in Rule 6.508(D) constitutes an adequate and independent ground on which the Michigan courts may rely in foreclosing review of federal claims. Howard, 405 F.3d at 477.
Nonetheless, again, the district court opted to ignore the defense in favor of addressing the merits of Akrawi's claim, "in the interest of judicial economy." In defense of this ruling, Akrawi argues that even if procedural default is in play, his default is excused by an adequate showing of "cause and prejudice." See Coleman, 501 U.S. at 750, 111 S.Ct. 2546 (recognizing that the procedural bar can be avoided if the petitioner "can demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law"). Akrawi contends the "cause and prejudice" requirements are satisfied by the same facts that establish his habeas claim, i.e., the prosecution's active concealment of its Brady violation, which deprived him of a fair trial. He correctly argues that evaluating the cause-and-prejudice requirements requires an analysis that mirrors the analysis implicated by the merits of Akrawi's habeas claim, thus revealing the wisdom in the district court's "judicial economy" rationale. Indeed, the Sixth Circuit adopted this very approach under very similar circumstances in Bell v. Bell, 512 F.3d 223 (6th Cir.2008) (en banc):
"[T]he cause and prejudice standard tracks the last two elements of a Brady claim: suppression by the government and materiality.... We therefore choose to focus our attention on the merits of Bell's claim with the understanding that our decision on the merits resolves any issues as to procedural default."
Id. at 231 n. 3 (citations omitted).
We adopt the same approach in this case, looking past procedural default to address the merits, because Akrawi, if he *262 succeeds in showing suppression of favorable evidence material to guilt or innocence, will have necessarily shown cause and prejudice excusing his procedural default.

C. Merits of the Brady Claim

1. Standard of Review

There is no dispute about the standard of review. AEDPA applies. It follows that although the Court reviews the district court's legal conclusions de novo and its fact findings for clear error, the Court may not grant habeas relief unless the state court's decision was "contrary to, or 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." Irick v. Bell, 565 F.3d 315, 319-20 (6th Cir.2009) (quoting 28 U.S.C. § 2254(d)(1)-(2)). In applying clearly established Supreme Court precedent, the court looks to the holdings, as opposed to dicta, of the Supreme Court's decisions as of the time of the relevant state-court decision. Lockyer v. Andrade, 538 U.S. 63, 71, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003).
The governing substantive standards are also summarized in Irick:
In Brady [v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963)], the Supreme Court held "that the suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution." Id. at 87, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215. "`There are three components of a true Brady violation: the evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued.'" Owens [v. Guida], 549 F.3d [399] at 415 [(6th Cir.2008)] (quoting Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)). A defendant is prejudiced when there is "a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Kyles v. Whitley, 514 U.S. 419, 433-34, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).
Irick, 565 F.3d at 321.
The extent to which the rule of Brady requires disclosure not just of evidence of formal cooperation agreements, but also evidence of informal communications between the prosecution and a witness, has received significant attention in recent Sixth Circuit case law. In Bell v. Bell, the court noted that "[i]t is well established that an express agreement between the prosecution and a witness is possible impeachment material that must be turned over under Brady." 512 F.3d at 233. However, "[t]he existence of a less formal, unwritten or tacit agreement is also subject to Brady's disclosure mandate." Id. (citing Wisehart v. Davis, 408 F.3d 321, 323-24 (7th Cir.2005)). "Brady is not limited to formal plea bargains, immunity deals or other notarized commitments. It applies to `less formal, unwritten, or tacit agreement[s],' so long as the prosecution offers the witness a benefit in exchange for his cooperation, ... so long in other words as the evidence is `favorable to the accused.'" Harris v. Lafler, 553 F.3d 1028, 1034 (6th Cir.2009) (quoting *263 Bell, 512 F.3d at 233, and Bagley, 473 U.S. at 678, 105 S.Ct. 3375).
Yet, the mere fact that a witness desires or expects favorable treatment in return for his testimony is insufficient; there must be some assurance or promise from the prosecution that gives rise to a mutual understanding or tacit agreement. Bell, 512 F.3d at 233. Further, the mere fact of favorable treatment received by a witness following cooperation is also insufficient to substantiate the existence of an agreement. "[I]t is not the case that, if the government chooses to provide assistance to a witness following trial, a court must necessarily infer a preexisting deal subject to disclosure under Brady." Id. at 234. "The government is free to reward witnesses for their cooperation with favorable treatment in pending criminal cases without disclosing to the defendant its intention to do so, provided that it does not promise anything to the witness prior to the testimony." Id. (quoting Shabazz v. Artuz, 336 F.3d 154, 165 (2d Cir.2003) (emphasis in original)).

2. Mutual Understanding

Applying these standards, the question emerges whether the prosecution made assurances or representations to Abood suggesting the existence of a mutual understanding or tacit agreementevidence favorable to Akrawi because of its impeachment value. The district court, after considering the evidence presented at trial and the later evidentiary hearing, answered this question in the affirmative. It concluded that while there was no formal agreement between Abood and Macomb County officials, there was an informal agreement to reduce the charges against him in return for his testimony. The court concluded that the Michigan appellate court's contrary conclusion was based on an unreasonable application of clearly established federal law.
Indeed, the Michigan appellate court's analysis seems to have been based on two fundamental errors of law. First, the appellate court recognized a duty to disclose only formal plea agreements approved by the prosecutor. Yet, as Bell recognizes, even unspoken, tacit agreements or mutual understandings may constitute evidence favorable to the accused that must be disclosed. Second, the Brady disclosure requirement "applies to relevant evidence in the hands of the police, whether the prosecutors knew about it or not, whether they suppressed it intentionally or not, ... and whether the accused asked for it or not." Harris, 553 F.3d at 1033. The notion, relied on by the Michigan appellate court, that communications by police officers need not be disclosed unless approved by the prosecutor flies in the face of the prosecutor's "duty to learn of any favorable evidence known to others acting on the government's behalf ... including the police." Id. (quoting Strickler, 527 U.S. at 280-81, 119 S.Ct. 1936).
Moreover, the district court's determination that communications between Pappas, Fresard and Suhy, on behalf of the prosecution, and Abood and his attorney Halpern gave rise to an informal agreement, or mutual understanding, is well supported by the record. Even though Pappas, Fresard and Suhy consistently maintained that no promises or express agreements were made, and even if this testimony were accepted on its face as true, the fact remains that all three acknowledged understanding that Abood's cooperation could result in reduction of the charges against him ... an understanding consistent with Abood's and Halpern's manifest understandingi.e., a tacit but mutual understanding. The prosecution team's knowledge of this mutual understanding, *264 stemming from communications between the prosecution and Abood and his counsel, represents knowledge of communications that could have been used by Akrawi in impeaching Abood and therefore constitutes "Brady material" that should have been disclosed. See Harris, 553 F.3d at 1033 (holding that statements by police to witness that his girlfriend would be released if they were satisfied with his cooperation, that he would be released if he testified consistently at a preliminary examination, and that he should not tell anyone about the police promises constituted Brady material the nondisclosure of which resulted in cognizable prejudice requiring habeas relief).
Accordingly, we hold that the Michigan appellate court's ruling that the prosecution did not breach its duty under Brady represents an unreasonable application of clearly established federal law.[6]

3. Prejudice

Yet, the prosecution's violation of its Brady duty of disclosure warrants habeas relief only if there is "a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Kyles, 514 U.S. at 433-34, 115 S.Ct. 1555. On this point, the district court agreed with the Michigan Court of Appeals that Akrawi was not prejudiced by the prosecution's misconduct.[7] The two courts agreed that although no direct evidence of an informal agreement or mutual understanding between Abood and the prosecution was introduced, the jury heard substantial evidence of the potential for a charge-reduction deal. Indeed, as the foregoing summary of relevant trial proceedings demonstrates, Akrawi's counsel did not fail to take advantage of this evidence to impugn Abood's credibility. Howarth's cross-examination of Abood would arguably have been more effective if evidence of the mutual understanding had been disclosed prior to trial, but only incrementally so. There is no reason to believe that disclosure of the additional impeachment evidence would have so altered the jury's assessment of Abood's already suspect credibility as to give rise to a reasonable probability that the outcome of the trial would have been different.
Further, both the district court and the Michigan appellate court recognized that the prosecution's case against Akrawi was not totally dependent on Abood's testimony. Even more damning was the testimony of Rene Arias, who also implicated Akrawi in significant cocaine trafficking. Thus, unlike the situation posed in Harris, 553 F.3d at 1034, where the nondisclosure of impeachment evidence was deemed to cause actual prejudice because the prosecution's case hinged on the testimony of one witness, Abood's testimony *265 was not the "centerpiece" of the prosecution's case against Akrawi.
Akrawi recognizes the importance of Arias's testimony, but argues that Arias's credibility, like Abood's, is suspect. Akrawi insists that there was little physical evidence linking him to the conspiracy, that the prosecution's case was based largely on suspect testimony of cooperating accomplices, and that the evidence against him was not overwhelming. Still, the nondisclosure of the mutual understanding with Abood has not been shown to be such a failure as to "put the whole case in such a different light as to undermine confidence in the verdict." Kyles, 514 U.S. at 435, 115 S.Ct. 1555. Considering the trial evidence collectively, as the court must, see id. at 436, 115 S.Ct. 1555, it can hardly be said that the state appellate court's conclusion on the question of actual prejudice represents an unreasonable application of Supreme Court precedent. The district court's concurrence in the state court's analysis of the prejudice element must therefore be upheld.

4. Structural Error

Akrawi insists that this is no ordinary Brady violation. Not only did the prosecution suppress impeachment evidence, but, Akrawi argues, the prosecution also sponsored perjured testimony to conceal the suppressed evidence, thereby compounding the wrong. This "Brady-plus" prosecutorial misconduct is said to amount to "structural error" that demands relief to vindicate the integrity of the judicial process, irrespective of a showing of actual prejudice.
A false-testimony claim is cognizable in habeas because the "deliberate deception of a court and jurors by the presentation of known false evidence is incompatible with rudimentary demands of justice." Abdus-Samad v. Bell, 420 F.3d 614, 625 (6th Cir.2005) (quoting Giglio v. United States, 405 U.S. 150, 153, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972)). To prevail on such a claim, Akrawi must show "(1) that the prosecution presented false testimony (2) that the prosecution knew was false, and (3) that was material." Id. at 625-26. The subject statement must be "indisputably false" rather than "merely misleading." Id. at 626 (quoting Byrd v. Collins, 209 F.3d 486, 517-18 (6th Cir.2000)).
Akrawi identifies as perjured testimony (1) Abood's testimony that he was not promised anything in return for his testimony, which was falsely corroborated by Pappas, Fresard and Suhy; and (2) the testimony of Pappas and Fresard to the effect that they lacked authority to grant Abood a charge-reduction, which was refuted by Marlinga's 2007 affidavit. With respect to the first item, we conclude, viewing the record as a whole, that the no-promise-or-agreement testimony was misleading, but has not been shown to be undisputably false. Inasmuch as there appears to have been no express promise or agreement, the testimony was technically accurate. While the record clearly shows that both Abood and members of the prosecution team understood or expected that Abood's cooperation would or could result in a reduction of the charges pending against him, there is scant evidence of an actual meeting of the minds.
As to the second item, Marlinga's late-filed affidavit creates a question regarding the truthfulness of Pappas's and Fresard's testimony that they lacked authority; it does not establish perjury. The weight to be assigned to the Marlinga affidavit is a threshold question. We note that Marlinga did not testify at trial or in the evidentiary hearing. He was never subject to cross-examination. The Marlinga affidavit was filed in the district court sixteen years after the subject Akrawi investigation and *266 prosecution and just days before the district court issued its ruling on the habeas petition. It was simply filed, without explanation. No leave to supplement the record with newly discovered evidence was sought or obtained. Yet, no objection was or has been interposed by the Warden. Nor has the Warden attempted to otherwise respond to the contents of the affidavit. In sum, we find no reason to give Marlinga's sixteen-year-old memory controlling weight over the arguably contrary testimony of Pappas and Fresard given at trial in 1991 and in the evidentiary hearing in 2001.
Further, even if Marlinga did delegate charge-reduction authority to Pappas and Fresard, and they knew it, they could have been understandably reluctant to exercise it by making promises to an offender facing life in prison without supervisory approval. It is entirely plausible, in other words, that they believed and acted as though they lacked actual authority, despite Marlinga's attempt to delegate it. Moreover, even assuming Pappas and Fresard knowingly testified falsely as to their authority, their false statements are hardly "material." Irrespective of their authority, the record is clear that they did not exercise it by making any express quid pro quo promise or agreement prior to Abood's trial testimony. And if they had testified that they did have authority and did make comments or representations about the possibility of future favorable treatment that may have induced Abood's cooperation, then the record would not have been materially changed, because, as discussed above, the jury heard significant testimony of both their understanding and Abood's understanding that Abood's cooperation could result in leniency.
It follows that the factual discrepancies which Akrawi calls prosecution-sponsored perjury are of relatively minor significance. They are not indicative of the sort of "structural error" that could justify automatic reversal. See United States v. Kuehne, 547 F.3d 667, 681 (6th Cir.2008) ("Structural errors reflect `a defect affecting the framework within which the trial proceeds, rather than simply error in the trial process itself.'"); United States v. Kimbrel, 532 F.3d 461, 469 (6th Cir.2008) (defining structural errors as errors that affect the "entire conduct of the trial from beginning to end"); Hereford v. Warren, 536 F.3d 523, 529 (6th Cir.2008) (noting that structural error has been found "only in a very limited class of cases").

III. CONCLUSION
In sum, petitioner Akrawi has succeeded in demonstrating that the prosecution violated the rule of Brady by suppressing evidence of its communications with Abood that were mutually understood as justifying the expectation that his cooperation could result in a reduction of the charges against him. He has failed to demonstrate, however, that this nondisclosure resulted in such actual prejudice as to warrant habeas relief. He has also failed to show structural error warranting automatic reversal. The district court's holding that the Michigan appellate court did not unreasonably apply clearly established federal law in denying Akrawi relief from judgment is therefore AFFIRMED.
NOTES
[*]  The Honorable James L. Graham, United States District Judge for the Southern District of Ohio, sitting by designation.
[1]  The sentence was subsequently reduced due to a change in Michigan law and Akrawi was released on parole from the Michigan Department of Corrections on December 2, 2008. Akrawi's release from imprisonment does not affect his entitlement to seek habeas relief because (1) his incarceration at the time he filed his habeas petition satisfies the "in custody" requirement; and (2) a parolee is still "in custody" for habeas purposes. Abela v. Martin, 380 F.3d 915, 921 (6th Cir.2004).
[2]  Abood spelled his name in this manner when he testified in trial. In a later-filed affidavit, his names appears as "Wissam Abbod." The district court noticed the discrepancy and, consistent with the parties' briefing, elected to use "Abood," a practice continued in this opinion.
[3]  The impact on Abood's family remained undefined in the record because the trial court sustained Howarth's objection to the prosecutor's question in this regard.
[4]  The operative term in the second sentence quoted is missing in the original. Yet, whether the missing term is "the agreement of" or "the willingness of" or "the intention of," the meaning seems plain. Halpern appears to have understood that his client stood to gain a charge-reduction in some degree, depending on the extent of his assistance.
[5]  By the time the district court addressed the merits of the habeas petition, Akrawi had further supplemented the record with the affidavit of former Macomb County Prosecuting Attorney Carl Marlinga. The affidavit was signed on June 13, 2007 and filed in the district court on June 14. The filing of the affidavit was not objected to by the Warden, and the district court received it and considered it without any comment on its untimeliness.

Marlinga attests that, in connection with Abood's cooperation, he made an exception to his standing policy regarding plea bargains with major drug dealers. Specifically, he delegated his authority to approve a reduction in charges to officials managing the Akrawi investigation, i.e., Pappas and Fresard. While Marlinga does not know what promises were made and does not believe any express agreement or promise was made, he confirms that his "representatives were authorized to give Abood reason to believe that if he delivered, we would deliver."
Marlinga's affidavit does not substantiate the existence of an express agreement, but contradicts Fresard's and Pappas's testimony that they lacked authority to enter into a charge-reduction agreement and tends to undermine their credibility.
[6]  This scope of Brady's requirements was clearly established when the Michigan Court of Appeals ruled in December 2003. In analogous circumstances, the Harris court, applying AEDPA review, held a contrary 2001 Michigan Court of Appeals ruling to be an unreasonable application of clearly established federal law. Inasmuch as Harris stands for the proposition that Brady's application to tacit agreements was clearly established in 2001, it must be deemed clearly established in 2003 as well. See Smith v. Stegall, 385 F.3d 993, 998 (6th Cir.2004) ("We are bound by any prior Sixth Circuit decisions concluding that federal law on a particular issue has been `clearly established' by certain holdings of the Supreme Court.").
[7]  The Oakland County Circuit Court, in originally finding a Brady violation and granting relief from judgment, did not expressly consider whether the violation resulted in prejudice. Thus, no court that has visited the issue has found cognizable prejudice to Akrawi.
