OPINION
In this case, an internal investigation by the U.S. Attorney’s Office found evidence suggesting that during the trial of. Petitioner-Appellant Kenneth Jefferson (“Jefferson”) on drug-conspiracy charges, the prosecution failed to disclose to the defense the extent of the promises of leniency that the prosecution made to several cooperating witnesses. In a motion to vacate his sentence filed pursuant to 28 U.S.C. § 2255, Jefferson alleged that he was denied a fair trial because the prosecutor violated his obligation under Brady v. Maryland to disclose material impeachment evidence. Although the district court initially denied Jefferson’s motion, *541we remanded the case so that the district court could make additional findings of fact regarding whether some of Jefferson’s claims were filed within the statute of limitations, and whether equitable tolling should be applied. On remand, the district court again denied Jefferson’s motion, finding that Jefferson’s claims were not timely filed, that equitable tolling was not warranted, and that even if timely, Jefferson’s Brady claims failed on the merits. We reject the district court’s conclusion that Jefferson failed to exercise due diligence in these circumstances, and hold that a § 2255 petitioner is permitted to rely on the government’s representation that it has fulfilled its Brady obligations. Reasonable diligence does not require a § 2255 petitioner repeatedly to scavenge for facts that the prosecution is unconstitutionally hiding from him. Nonetheless, assuming that Jefferson’s claims were timely filed, we agree with the district court that Jefferson’s Brady claims fail on the merits, because the undisclosed impeachment evidence was not prejudicial. Accordingly, we AFFIRM the judgment of the district court.
I. BACKGROUND
This appeal stems from Jefferson’s conviction in June 1999 for conspiring to distribute and to possess with intent to distribute cocaine and cocaine base in violation of 21 U.S.C. §§ 841(a)(1) and 846. See United States v. Stines, 313 F.3d 912, 913 (6th Cir.2002). The evidence at trial established that Jefferson was part of a gang organized in the late 1980s in Ypsilanti, Michigan, by codefendant Joseph Stines (“Stines”) for the purpose of processing and distributing crack cocaine. See id. at 914. In statements to law enforcement agents following his arrest, Jefferson “admitted that he had started selling crack in Ypsilanti in the summer of 1996,” that “[an unindicted coconspirator] was one of his principal suppliers!,] and that he often bought one-eighth of a kilogram, but on two occasions he had purchased a half kilogram.” Id. at 915.
Several coconspirators, including Tali Alexander (“Alexander”), Reese Palmer (“Palmer”), Rasul Warren (“Warren”), and Eva Taylor (“Taylor”), cooperated with the government in exchange for favorable plea agreements and testified as to the nature of the conspiracy and defendants’ connections to it. On cross-examination, these witnesses testified that the sentences the government agreed to recommend pursuant to the plea agreements were far lower than the sentences they would face for the full scope of criminal activity to which each admitted. Another witness, Samuel Mul-lice (“Mullice”), testified that in 1996 Jefferson gave him a ride home from the parole office and told Mullice that “he was doing something” and that if Mullice “need[ed] to do something, get in contact.” R. 331 (Trial Tr. at 2767) (Page ID # 6749). Mullice interpreted this statement to mean that Jefferson was selling drugs. Id. at 2768 (Page ID # 6750). Witness Labron Nunn (“Nunn”) testified that in 1997 he bought two and a half ounces of crack cocaine from Jefferson, and that Jefferson asked Nunn to join “the family.” Stines, 313 F.3d at 915. The jury returned a verdict of guilty as to all defendants, and Jefferson was sentenced to 240 months of imprisonment, followed by five years of supervised release.
In July 1999, one of Jefferson’s codefen-dants filed a motion for a new trial, joined by Jefferson, asserting that their trial was tainted by prosecutorial misconduct because “the government clearly had either a tacit agreement or an overt agreement with ... witnesses [including Alexander] that they would receive certain additional consideration following their testimony which they did not reveal and which the Government did not reveal.” R. 209 (Mot. *542for New Trial at 5) (Page ID # 9090). The district court denied the motion for a new trial. R. 240 (Dist.Ct.Order) (Page ID # 9259). The following year, in June 2000, Stines filed a renewed motion for a new trial, which Jefferson joined. See R. 305 (Am. Mot. for New Trial) (Page ID # 9749). The amended motion repeated the allegation that the prosecution failed “to disclose the full extent of their agreements with the[ ] witnesses” who testified against the defendants, including Alexander, Warren, and Palmer, and that the prosecutor “knowingly allowed perjured testimony to be given.” Id. at 19 (Page ID # 9772). This motion was not considered on the merits by the district court, because at the time the motion was filed, the case was already on appeal. See R. 370 (Dist.Ct.Order) (Page ID # 10201).
In 2002, we affirmed Jefferson’s conviction and sentence on direct appeal. Stines, 313 F.3d at 913. Jefferson was not a party to the petition for a writ of certiorari from the Supreme Court filed by some of his codefendants, and accordingly, Jefferson’s “conviction became final on May 12, 2003, upon the expiration of the 90-day period for seeking the writ.” Jefferson v. United States, 392 FedAppx. 427, 429 (6th Cir.2010). Jefferson filed a motion to vacate his sentence under 28 U.S.C. § 2255 on August 26, 2004, raising four grounds for relief. R. 486 (§ 2255 Pet.) (Page ID #213). Jefferson concedes that these claims were untimely under § 2255(f)(1), and he does not pursue any of these claims in the instant appeal. Appellant Br. at 11; see Jefferson, 392 Fed.Appx. at 429.
In March 2004, five months before Jefferson filed his initial § 2255 motion, Alexander, in a letter to the district judge presiding over his criminal case, stated that he had expected AUSA Richard Con-vertino (“Convertino”), the prosecutor in charge of his case (and in charge of Jeffer--son’s and Stines’s prosecutions), to make a recommendation for a downward departure to reduce Alexander’s sentence. Jefferson, 392 FedAppx. at 432. This letter prompted a closer look at the Alexander case, and the district court identified an absence of downward departure motions and yet sentences were below amounts identified in plea agreements. Subsequently, the U.S. Attorney’s Office (“USAO”) began an internal investigation into Convertino’s conduct in the Alexander case. Interviews with witnesses Alexander, Warren, Palmer, and Hans Thomas (“Thomas”), who also testified in Jefferson’s trial, revealed that they had all been sentenced far below the downward-departure sentences the government had agreed to recommend in their respective plea agreements, and extremely far below the maximum sentences agreed to in the plea agreements. The investigation culminated in a report known as the Schools Memorandum, which we previously summarized as follows:
Without recounting the information set forth in that Memorandum, we note that it suggests there is evidence that Con-vertino met with some cooperating witnesses in this case without defense counsel; entered written plea agreements and made some, at least tacit, promises of further sentencing reductions; had witnesses testify without revealing the additional understandings; moved orally at sentencing or in Rule 35 motions for downward departures; and had the sentencing records of these witnesses sealed. The fairness of Jefferson’s trial was not the focus of the investigation, but it produced evidence that the government felt compelled to disclose to Jefferson.
Jefferson, 392 Fed.Appx. at 432. Adding to concerns regarding Convertino’s conduct as an AUSA was United States v. Koubriti, in which the district court dismissed — with the agreement of the gov*543ernment — terrorism charges against several convicted defendants. The district court in Koubriti found that the prosecutors, including Convertino, failed to turn over exculpatory evidence to the defense and “materially misled the Court, the jury and the defense as to the nature, character and complexion of critical evidence that provided important foundations for the prosecution’s case.” 336 F.Supp.2d 676, 680-81 (E.D.Mich.2004).
On March 25, 2005, Jefferson filed an Amended Motion for New Trial or in the Alternative Defendant’s Renewed Motion for Mistrial and for Evidentiary Hearing and a Motion to Recall Mandate or, In the Alternative, Motion under Fed.R.Civ.P. 60(b)(5) (together, the “March 2005 motions”). R. 517 (Am. Mot. for New Trial) (Page ID # 691); R. 519 (Mot. to Recall) (Page ID # 717). Jefferson’s amended motion for a new trial was a verbatim repetition of Stines’s 2000 Amended Motion for a New Trial. The 2005 motion (consisting of a photocopy of Stines’s 2000 motion) stated that “Defendant has recently discovered that the Government made additional deals with various witnesses which was withheld .from the Defendant.” R. 517 (Am. Mot. for New Trial at 2) (Page ID # 692). Jefferson’s motion to recall the mandate asserted a new claim that Nunn provided perjured testimony at trial that was contradicted by his testimony at an earlier trial. R. 519 (Motion to Recall at 2) (Page ID # 718). Both of these motions were construed by the district court as motions to amend Jefferson’s initial § 2255 motion.1 R. 533 (Mag. J. R & R at 1) (Page ID # 784); R. 614 (Dist. Ct. Op. at 1-2) (Page ID # 2391-92).
Six months after Jefferson filed these motions, on September 30, 2005, the government disclosed to Jefferson memoranda of interviews with Thomas, Warren, and Alexander conducted in late 2004 in connection with the internal investigation into Convertino’s conduct. See Appellant Br. at 14-15. Following these disclosures, as well as Stines’s counsel’s efforts to unseal sentencing records for several of the witnesses who testified at Stines’s and Jefferson’s trial, Stines filed a supplemental motion on March 27, 2006, adding to his previously filed § 2255 motion. See R. 552 (Supp. Arguments in Supp. of Pet.) (Page ID # 913). Jefferson obtained counsel in January 2006, and that counsel filed a motion to join Stines’s supplemental briefing on September 26, 2006. R. 573 (Notice of Joinder) (Page ID # 1270).
The district court denied Jefferson’s § 2255 motion and the March 2005 motions to amend as untimely. R. 614 (Dist. Ct. Op. at 24) (Page ID # 2414). Jefferson had argued that his claims regarding pros-ecutorial misconduct were timely because they could not have been discovered until either (i) September 2, 2004, when the unrelated terrorism Koubriti decision was issued, finding that Convertino had failed to disclose exculpatory evidence, or (ii) September 30, 2005, when the government disclosed its interviews with witnesses from Jefferson’s trial. The district court rejected both of these triggering dates. First, the district court found that a decision in an unrelated terrorism case could not constitute the factual predicate for prosecutorial-misconduct claims in Jefferson’s case. Id. at 22 (Page ID #2412). Second, the court found that the September 30, 2005 disclosures could not form the basis of Jefferson’s § 2255 motion, because Jefferson filed his motions in March 2005, *544 before the September 2005 disclosures. Id.
On appeal, we reversed and remanded. Jefferson, 392 Fed.Appx. at 433. We agreed with the district court that Jefferson could not rely on the September 2, 2004 dismissal of the terrorism charges in Koubriti as the factual predicate of his claims. Id. at 431. We also agreed that Jefferson could not use the September 2005 disclosures as the basis for his March 2005 motions. See id. We concluded, however, that the district court “did not resolve the critical question of whether Jefferson’s additional claims were brought within one year of ‘the date on which the facts supporting the claim or claims presented could have been discovered through the exercise of due diligence.’ ” Id. (quoting 28 U.S.C. § 2255(f)(4)). We thus remanded “for further consideration of the statute of limitations and the possible application of equitable tolling.” Id. at 427.
On remand, the district court again denied Jefferson’s § 2255 motion. The district court found that Jefferson’s claims were untimely and were not subject to eqúitable tolling, and that even if the claims were timely, they failed on the merits. This appeal followed.
II. ANALYSIS
A. Standard of Review
“In reviewing the denial of a 28 U.S.C. § 2255 motion, we apply a de novo standard of review to the legal issues and uphold the factual findings of the district court unless they are clearly erroneous.” Hamblen v. United States, 591 F.3d 471, 473 (6th Cir.2009). We review de novo the district court’s determination regarding the applicability of equitable tolling when the facts are undisputed. Solomon v. United States, 467 F.3d 928, 932 (6th Cir. 2006).
B. Statute of Limitations
“A motion filed pursuant to 28 U.S.C. § 2255 is subject to a one-year statute of limitations, with the limitations period beginning to run ‘from the latest of four possible dates.” Benitez v. United States, 521 F.3d 625, 629 (6th Cir.2008). At issue in this case is whether Jefferson filed his claims within one year of “the date on which the facts supporting the claim or claims presented could have been discovered through the exercise of due diligence.” 28 U.S.C. § 2255(f)(4). This standard “does not require the maximum feasible diligence, only due, or reasonable, diligence.” DiCenzi v. Rose, 452 F.3d 465, 470 (6th Cir.2006) (internal quotation marks omitted). “ ‘[T]he petitioner bears the burden of proving that he exercised due diligence.’ ” Johnson v. United States, 457 Fed.Appx. 462, 468 (6th Cir.2012) (quoting DiCenzi, 452 F.3d at 471). Accordingly, the key question is whether, taking into account “the reality of the prison system,” DiCenzi, 452 F.3d at 470 (internal quotation marks omitted), Jefferson could have discovered the factual predicate for his claims using due diligence more than a year before filing his March 2005 motions, supplemented by his September 2006 filing.
1. Brady Claims
Jefferson argues that he could not have discovered the facts underlying his claims earlier than March 2005 because Convertino deliberately hid the plea agreements and sentencing records of the cooperating witnesses. R. 667 (Pet.’s Br. After Remand at 4) (Page ID #3513). The district court rejected this argument and found that using due diligence, Jefferson could have discovered the facts underlying the claims raised in his March 2005 motions more than a year before he filed the motions. The district court faulted Jeffer*545son for failing to attempt to investigate further his suspicions of prosecutorial misconduct and failing to seek out sources other than the government to acquire facts and evidence to substantiate his suspicions. We hold that, given the record in this case, the district court’s determinations are erroneous: Section § 2255(f)(4)’s requirement that a petitioner exercise reasonable diligence to discover the factual predicate underlying his claims does not require a petitioner repeatedly to seek out information that the government unconstitutionally failed to disclose despite having notice that petitioner sought the very information suppressed.
We must determine what diligence a reasonable person in Jefferson’s circumstances would have exercised to discover the facts underlying his claim that the prosecution withheld information relating to promises made to government witnesses. Prior to Jefferson’s trial, the defense requested “information relating to ... any consideration, reward, agreement, or promise ... given by the government to [any witness that the government intends to call at trial].” R. 97 (Mot. for Discovery at 5) (Page ID # 9039). In response, the government represented that it was “aware of its duties under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and will provide impeachment information as contemplated in Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).” R. 139 (Gov’t Resp. to Def.’s Various Mots, for Discovery at 1-2) (Page ID #8875-76). After their convictions, in July 1999 and again in June 2000, the defendants filed motions for a new trial, each of which explicitly raised the claim that the government had failed to disclose the full extent of the promises made to cooperating witnesses. See R. 209 (Mot. for New Trial at 5) (Page ID # 9090); R. 305 (Am. Mot. for New Trial at 19) (Page ID # 9772). The government responded to both motions, arguing that defendants’ challenges regarding the impeachment of government witnesses lacked merit and were based on pure speculation. See R. 213 (Gov’t Resp. in Opp. to Def.’s Mot. for New Trial) (Page ID # 9116); R. 349 (Gov’t Resp. to Def.’s Am. Mot. for New Trial at 2-3) (Page ID # 10264-65). This procedural history demonstrates both that the prosecution was clearly on notice that the defendants sought all information relating to promises made to government witnesses, and that the prosecution made a representation that it would disclose all impeachment evidence in its possession to the defense.
The Supreme Court has held that a defendant may rely on exactly this kind of representation of full disclosure by the government, and that a defendant may “assume that his prosecutors would not stoop to improper litigation conduct to advance prospects for gaining a conviction.” Banks v. Dretke, 540 U.S. 668, 694, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004). Accordingly, given the prosecution’s representation that it would disclose impeachment evidence, a defendant such as Jefferson “had no basis for believing [the prosecution] had failed to comply with Brady.” Strickler v. Greene, 527 U.S. 263, 287, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). In Banks, despite representing to the defendant that the government would “provide her with all discovery to which [she was] entitled,” the government failed to disclose certain evidence that would have aided the defense in impeaching the government’s witnesses. Banks, 540 U.S. at 675, 124 S.Ct. 1256. Further, at trial, “the prosecution raised no red flag when the informant testified[] untruthfully.” Id. The Court rejected the Fifth Circuit’s conclusion that the defendant was not sufficiently diligent in pursuing her post-conviction claims because she did not seek out evidence to support her claim of a Brady violation. Id. at 688, 698, 124 *546S.Ct. 1256. Specifically, the Court rejected the position “that the prosecution can lie and conceal and the prisoner still has the burden to ... discover the evidence, ... so long as the potential existence of a prosecutorial misconduct claim might have been detected.” Id. at 696, 124 S.Ct. 1256 (internal quotation marks and citation omitted). The Court concluded that “[a] rule thus declaring ‘prosecutor may hide, defendant must seek,’ is not tenable in a system constitutionally bound to accord defendants due process.” Id.
Likewise, in Strickler, the Court explained that “[t]he presumption, well established by tradition and experience, that prosecutors have fully discharged their official duties, is inconsistent with the novel suggestion that [a] conscientious [defendant] [has] a procedural obligation to assert constitutional error on the basis of mere suspicion that some prosecutorial misstep may have occurred.” 527 U.S. at 286-87, 119 S.Ct. 1936. Especially when the prosecutor “was an active participant in shielding any evidence of the facts underlying the [Brady] claim,” a prisoner does not have a burden to investigate whether there exists evidence that the government had a constitutional obligation to disclose, but did not. Douglas v. Workman, 560 F.3d 1156, 1181 (10th Cir.2009) (holding that petitioner could not, “exercising due diligence,” have “uncovered the existence of a deal” between the prosecutor and a cooperating witness any sooner); see United States v. Tavera, 719 F.3d 705, 711-12 (6th Cir.2013) (rejecting a rule that would require defendants to exercise due diligence to discover exculpatory evidence in the government’s possession); Stams v. Andrews, 524 F.3d 612, 619 (5th Cir.2008) (holding that “there was no requirement that [petitioner] act diligently to investigate further assuming the state could be taken at its word”).
Accordingly, the government’s position that Jefferson failed to exercise due diligence because he did not seek information “the very existence of which the [government] had improperly withheld in violation of Brady ---- is fundamentally at odds with’ Brady itself.” Willis v. Jones, 329 Fed.Appx. 7, 16-17 (6th Cir.2009). The prosecution in Jefferson’s trial had a constitutional obligation to disclose the full extent of the consideration given to the cooperating witnesses in exchange for their testimony. This obligation existed regardless of whether the defendants in Jefferson’s trial asked for the information- — -which they did, repeatedly. We hold that § 2255(f)(4)’s due-diligence standard did not require Jefferson continuously to seek out evidence that the government had a constitutional duty to disclose (evidence that, despite specific requests by the defense for the information, the government represented did not exist). We reject the district court’s determination that because Jefferson suspected undisclosed promises as early as 2000, his failure to seek information from “the cooperating witnesses themselves or their acquaintances” and his failure to seek sentencing records — which the prosecutor had sealed — rendered his diligence insufficient. We do not fault Jefferson for failing to scavenge for evidence of undisclosed promises when he already repeatedly asked for disclosure and the evidence was unconstitutionally withheld by the government.2
*547This holding, however, does not answer the factual question of when Jefferson could have discovered the factual predicate underlying the claims presented in his March 2005 motions, supplemented by his September 2006 filing. On the one hand, we reject Jefferson’s argument that he did not discover the factual predicate underlying his claims until September 30, 2005, when the government disclosed the witness interviews. In some circumstances, the statute of limitations under § 2255(f)(4) will not begin to run on a Brady claim until the suppressed evidence is disclosed by the government. See, e.g., Willis, 329 Fed.Appx. at 17; Rinaldi v. Gillis, 248 Fed.Appx. 371, 378 (3d Cir. 2007); Stams, 524 F.3d at 619. We need not consider whether these circumstances are present in this case, because Jefferson’s § 2255 motion was filed in March 2005, before the government disclosures in September 2005. As we explained in our prior consideration of Jefferson’s petition, Jefferson cannot “logically argue that he did not discover the facts supporting the claims presented in the March 2005 motions until after the government’s disclosures in September 2005.” Jefferson, 392 Fed.Appx. at 431.
On the other hand, we also reject the government’s argument that Jefferson “discovered facts underlying the § 2255 motions” as early as 1999 and 2000, when the motions for a new trial were filed. Appellee Br. at 20. The government’s position ignores the distinction between suspicions of misconduct and having sufficient facts to sustain a § 2255 motion. Generally, courts have held that “eonclusory allegations alone, without supporting factual averments, are insufficient to state a valid claim under § 2255.” United States v. Moya, 676 F.3d 1211, 1213 (10th Cir.2012) (citing United States v. Fisher, 38 F.3d 1144, 1147 (10th Cir.1994)); see also Lynn v. United States, 365 F.3d 1225, 1238 (11th Cir.2004) (holding that a § 2255 motion failed on the merits when the motion was supported by affidavits containing “nothing more than eonclusory allegations”); Randy Hertz & James S. Liebman, 1-11 Federal Habeas Corpus Practice & Procedure § 11.6 (2012) (explaining that the “Rules Governing Section 2254 Cases ... require the petitioner to ... ‘state the facts supporting each ground ’ ” for relief alleged by the petitioner (quoting Rule 2(c) of the Rules Governing Section 2254 Cases in the United States District Courts (2010))). We acknowledge that new information discovered “that merely supports or strengthens a claim that could have been properly stated without the discovery ... is not a ‘factual predicate’ for purposes of triggering the statute of limitations under § 2244(d)(1)(D).” Rivas v. Fischer, 687 F.3d 514, 535 (2d Cir.2012). However, we cannot accept the government’s argument that Jefferson had knowledge of the factual predicate underlying his Brady claim based on his unsubstantiated suspicion that the prosecution withheld evidence regarding deals with cooperating witnesses. This is especially so given the prosecution’s representation that it had fulfilled its obligations under Brady and Giglio to disclose impeachment evidence. We decline to interpret AEDPA’s competing requirements — the requirement to plead at least some facts and the requirement of filing within one year of discover*548ing the “vital facts” — so as to create a trap that renders litigation of a successful § 2255 claim effectively impossible. “Without a clear standard [as to when suspicion and hints ripen into a factual predicate], it is likely that when a prisoner spends a tremendous amount of time establishing the validity of the facts, a court may find that the initial piece of uncorroborated information would be deemed a ‘factual predicate’ to start the statute-of-limitations period; if, however, a prisoner instead chooses to submit an application with the same piece of ‘raw’ information, it may fail the fact-pleading requirement.” Limin Zheng, Actual Innocence as a Gateway through the Statute-of-Limitations Bar on the Filing of Federal Habeas Corpus Petitions, 90 Cal. L.Rev. 2101, 2135 (2002).
Although we do not decide at what point in time Jefferson could have discovered the factual predicate underlying his claims, we note that it was not until March 29, 2004, that Alexander wrote to the district court asking about the status of his sentencing reduction. And it was not until October 2004 that Stines filed a § 2255 motion raising the, Brady claim. After counsel was appointed for Stines in January 2005, following a motion by the government to appoint counsel, Stines’s counsel began to file motions to unseal the sentencing records of the relevant cooperating witnesses, in an effort to discover the facts about the consideration received by the witnesses. Given that, the factual development that ultimately uncovered the prosecutorial misconduct appears to have been ongoing from March 2004 through early 2005, and especially because “a due diligence inquiry should take into account that prisoners are limited by their physical confinement,”3 Moore v. Knight, 368 F.3d 936, 940 (7th Cir.2004), Jefferson’s motion, filed in March 2005, appears to have been filed within one year of when the factual predicate underlying his claims was discoverable using reasonable diligence. We need not conclusively decide this complicated factual question, however, because, even assuming Jefferson’s claims were timely filed, we agree with the district court that the claims fail on the merits.
2. Ineffective-Assistance-of-Counsel Claim
With respect to his ineffective-assistance-of-counsel claim, Jefferson argues that “the predicate fact was that Labron Nunn had testified for Convertino in USA v. Eric Hinton a few weeks before he testified against Petitioner Jefferson,” and that Jefferson did not discover this fact until the spring of 2006 when Hinton and Jefferson were in the same prison facility. Appellant Br. at 15. This argument is not persuasive, because Jefferson could have discovered that Nunn testified in the Hinton trial years before 2006. Specifically, Nunn was cross-examined during Jefferson’s trial regarding inconsistencies between Nunn’s testimony in the Hinton trial and his testimony at Jefferson’s trial, and regarding the fact that Convertino was involved in both cases. R. 334 (Trial Tr. at 3442-46, 3455-56) (Page ID # 4545-49, 4558-59). Accordingly, Jefferson was aware of the factual predicate — that Nunn testified in the Hinton trial and that his testimony may have been inconsistent with his testimony at Jefferson’s trial — at the time of Jefferson’s trial in 1999. Jefferson could have filed a claim of ineffective assistance of counsel based on counsel’s failure to get a copy of Nunn’s trial testimony in *549the Hinton trial years before Jefferson filed his ineffeetive-assistance-of-counsel claim in September 2006. Therefore, Jefferson’s ineffective-assistanee-of-counsel claim is untimely.
C. Equitable Tolling
The district court also was instructed by the prior panel to determine whether any of Jefferson’s claims were entitled to equitable tolling. “The one-year statute of limitations for filing a § 2255 petition is subject to equitable tolling.” Johnson, 457 Fed.Appx. at 469. “[Ejquitable tolling allows courts to toll a statute of limitations when a litigant’s failure to meet a legally-mandated deadline unavoidably arose from circumstances beyond that litigant’s control.” Robertson v. Simpson, 624 F.3d 781, 783 (6th Cir.2010) (internal quotation marks omitted). A petitioner is entitled to equitable tolling “only if he shows (1) that he has been pursuing his rights diligently, and (2) that some extraordinary circumstance stood in his way and prevented timely filing.” Holland v. Florida, 560 U.S. 631, 130 S.Ct. 2549, 2562, 177 L.Ed.2d 130 (2010) (internal quotation marks omitted). We have explained that courts should not be rigid in applying this standard and should “consider each claim for equitable tolling on a case-by-case basis.” Jones v. United States, 689 F.3d 621, 627 (6th Cir.2012). “The flexibility inherent in equitable procedure enables courts to meet new situations that demand equitable intervention, and to accord all the relief necessary to correct particular injustices.” Holland, 130 S.Ct. at 2563 (internal quotation marks and alterations omitted).
On appeal, Jefferson argues that the extraordinary circumstance that prevented him from timely filing his § 2255 motion was “the elaborate action[] taken by former prosecutor Convertino ... to hide promises made to the witnesses] in return for false testimony, and to suppress pending charges against Witnesses Mulliee and Nunn.” Appellant Br. at 18. Jefferson contends that Convertino’s concealment of sentencing records through sealing orders prevented him from accessing the relevant documents needed to pursue his Brady claims. In effect, Jefferson argues that the substance of his Brady claims — the withholding of relevant impeachment evidence — is the extraordinary circumstance that prevented him from timely filing. In certain circumstances, “the same facts supporting a Brady claim [will] also support the application of the doctrine of equitable tolling.” Wardlaw v. Cain, 541 F.3d 275, 279 (5th Cir.2008). This justification for equitable tolling cannot succeed in this case, however, because Jefferson filed his March 2005 motions before the sentencing records were unsealed, and before the government disclosed the results of its internal investigation. Accordingly, Jefferson cannot logically argue that he was prevented from filing his claims before the information regarding the hidden deals was disclosed to him. Additionally, if it were the case that the alleged prosecutorial misconduct prevented Jefferson from obtaining the facts supporting his Brady claim, then the statute of limitations under § 2255(f)(4) would not have been triggered until Jefferson discovered those relevant facts, which would permit him to timely file his motion. See Rinaldi 248 Fed. Appx. at 380. We therefore conclude that Jefferson has not established that he is entitled to equitable tolling.
D. Merits of Jefferson’s § 2255 Motion — Brady Claims
Jefferson argues that the district court erred when it determined that the Brady claims raised in his § 2255 motion failed on the merits. “To warrant relief under section 2255, a petitioner must demonstrate the existence of an error of *550constitutional magnitude which had a substantial and injurious effect or influence on ... the jury’s verdict.” Griffin v. United States, 330 F.3d 733, 736 (6th Cir.2003) (citing Brecht v. Abrahamson, 507 U.S. 619, 637, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)). In this case, Jefferson claims that his rights under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), were violated when the prosecutor failed to disclose the extent of the agreements he had made with several witnesses who testified at trial. Under Brady, “a defendant’s due process rights are violated if the prosecution suppresses material exculpatory evidence that is favorable to the defense.” Hanna v. Ishee, 694 F.3d 596, 610 (6th Cir.2012). “Likewise, the prosecution violates Brady if it ... fails to volunteer evidence not requested by the defense, or requested only generally.” Id. To succeed on a Brady claim, “a habeas petitioner must show that (1) the withheld evidence was favorable to the petitioner, (2) the evidence was suppressed by the government, and (3) the petitioner suffered prejudice.” Jells v. Mitchell, 538 F.3d 478, 501 (6th Cir.2008).
The first prong of the Brady test is met with respect to all of the witnesses with whom Jefferson alleges Convertino had undisclosed agreements, because a prosecutor’s duty under Brady extends to impeachment evidence in addition to exculpatory evidence. See Stickler, 527 U.S. at 280, 119 S.Ct. 1936. Both express agreements between the prosecution and cooperating witnesses, as well as “less formal, unwritten or tacit agreement[s]” are “subject to Brady’s disclosure mandate.” Bell v. Bell, 512 F.3d 223, 233 (6th Cir.2008) (en banc); see Giglio v. United States, 405 U.S. 150, 154-55, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972). Evidence that the witnesses in Jefferson’s trial were going to be granted more favorable deals than they disclosed could have been used to discredit their testimony to a greater degree than was possible without the impeaching evidence. Thus, Jefferson has demonstrated that the evidence allegedly withheld was favorable to him.
Nonetheless, we agree with the district court that for each of the witnesses at issue, Jefferson either failed to demonstrate the existence of an undisclosed agreement or failed to meet the prejudice prong of the Brady test. The prejudice analysis under Brady evaluates the materiality of the evidence. “Evidence is material under Brady if a reasonable probability exists that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” Jells, 538 F.3d at 501-02. “The question is not whether the defendant would more likely than not have received a different verdict with the evidence, but whether in its absence he received a fair trial, understood as a trial resulting in a verdict worthy of confidence.” Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). Accordingly, “ ‘where the undisclosed evidence merely furnishes an additional basis on which to challenge a witness whose credibility has already been shown to be questionable or who is subject to extensive attack by reason of other evidence, the undisclosed evidence may be cumulative, and hence not material.’ ” Byrd v. Collins, 209 F.3d 486, 518 (6th Cir.2000) (quoting United States v. Avellino, 136 F.3d 249, 257 (2d Cir.1998)); see Akrawi v. Booker, 572 F.3d 252, 264 (6th Cir.2009) (holding that when “the jury heard substantial evidence of the potential for a charge-reduction deal,” the failure of the prosecution to disclose an informal agreement with a witness did not meet the prejudice prong of the Brady analysis). We address below the testimony of each witness who allegedly had an undisclosed deal with the prosecution.
*5511. Tali Alexander, Reese Palmer, and Rasul Warren
The district court found that evidence of additional deals with witnesses Alexander, Palmer, and Warren, even if disclosed, would not have been material. We agree. Assuming that the impeachment evidence was suppressed, the evidence was not material because Alexander, Palmer, and Warren were each cross-examined regarding their deals with the government resulting in favorable sentences, as well as their willingness to he to prevent incarceration. See Brooks v. Tennessee, 626 F.3d 878, 891 (6th Cir.2010) (“assum[ing] without deciding that the evidence was suppressed” for purposes of a Brady analysis).
Alexander was cross-examined extensively on the fact that his testimony was made in exchange for a deal with the government to avoid a life sentence for shooting multiple people, including a police officer, and for drug and firearm offenses that he admitted he had committed. See R. 329 (Trial Tr. at 2534-41) (Page ID # 7170-77). Defense counsel made clear to the jury that Alexander had a strong incentive to testify to the prosecutors’ satisfaction:
Q: If for any reason the two [prosecutors] decide not to [make a motion for a downward departure], sir, you are looking at spending the rest of your life plus 10 years in a federal penitentiary, correct?
A. Right.
Q. To avoid that, sir, you will do anything to get out rather than spend the rest of your life in a federal penitentiary?
A. Yep.
Id. at 2541 (Page ID # 7177). Alexander also admitted that he repeatedly had lied to police officers, that he would lie to avoid criminal charges, and that he would lie to avoid receiving a life sentence. See id. at 2600-01 (Page ID # 7236-37); id. at 2673 (Page ID # 7309) (admitting that he “cooperated to keep from getting life”).
Similarly, Palmer was cross-examined about his motives for cooperating with the government and testifying against his co-conspirators. Palmer stated that he decided to cooperate after learning that he had unwittingly sold crack cocaine to an undercover police officer, stating, “I couldn’t deny it ... because the [undercover agent] was right before me.” R. 325 (Trial Tr. at 1970) (Page ID # 6482). The jury was aware that pursuant to his plea agreement, Palmer pleaded guilty to delivering only 13.57 grams of cocaine base and 225.75 grams of cocaine, even though he had informed police that he had been dealing cocaine in much larger quantities, upwards of three kilograms. See R. 327 (Trial Tr. at 2250-53) (Page ID # 7818-21). In other words, the jury was made aware that had Palmer not cooperated, he would face 324 to 405 months in prison. Id. at 2267 (Page ID # 7836). Instead, because he cooperated, Palmer received a plea agreement that ’ calculated an agreed-to guidelines range of seventy to eighty-seven months. Further, if the government was satisfied with Palmer’s cooperation, it agreed to recommend a downward departure to sixty months. Id. at 2267-70 (Page ID # 7835-38). Palmer also admitted to lying repeatedly to his parole officer about selling drugs to avoid additional penalties. R. 326 (Trial Tr. at 2211-13) (Page ID # 6722-24). Accordingly, the jury had reason to believe that Palmer had a strong incentive to give perjured or exaggerated testimony against the defendants in exchange for a more lenient sentence, and that he had a history of lying to law enforcement officers to protect himself.
Finally, Warren was cross-examined on his incentives for cooperating with the government. He stated: “The reason I coop*552erated that night. was because I was caught red handed for ounces of cocaine, and I was on parole and facing 50 years, and I think about my kids and my family and think about myself.” R. 335 (Trial Tr. at 3672) (Page ID # 5922). Warren admitted that his agreement with the government included a provision for the government to make a downward departure from a recommended sentence of twenty-two years to a recommended sentence of ten years in exchange for Warren’s cooperation. Id. at 3691-92, 3694 (Page ID #5941-42, 5944). Further, Warren testified that he had a history of lying to government agents, and he admitted that he would lie for the government in court to avoid going back to prison. Id. at 3708, 3808 (Page ID # 5958, 6058).
This summary of the relevant cross-examinations demonstrates that Alexander, Palmer, and Warren had their credibility impeached regarding their incentives to give favorable testimony in exchange for significantly more lenient sentences: Alexander was avoiding a life sentence in exchange for a downward departure that would leave the maximum sentence at twenty-five years; Palmer would receive a downward-departure recommendation for a sentence not to exceed five years, instead of facing between twenty-seven and thirty-three years in federal prison for larger drug quantities; and in exchange for Warren’s testimony, the government would recommend ten years in prison, rather than the twenty-two-year sentence he would face absent any cooperation. Despite the fact that these witnesses ultimately received even more lenient sentences, the jury already was aware of the witnesses’ significant motives to exaggerate or fabricate to please the government. Each witness also had admitted that he would lie to avoid harsh penalties. Accordingly, under our precedents, the additional basis on which to attack these witnesses’ credibility was not material, and Jefferson’s Brady claims regarding these witnesses fail. See Byrd, 209 F.3d at 518.
2. Labron Nunn and Samuel Mullice
The testimony of Nunn and Mullice at Jefferson’s trial helped connect Jefferson to the Stines conspiracy. Jefferson argues that the fact that both Nunn and Mullice were not charged or prosecuted for crimes they admitted to committing demonstrates that they had undisclosed agreements with Convertino. Appellant Br. at 33. The district court rejected this argument, finding that Jefferson’s claims regarding Nunn and Mullice were entirely speculative, and that Jefferson had presented no evidence to establish the existence of an undisclosed deal. We affirm the district court’s determination that Jefferson did not establish that a secret deal existed with respect either to Nunn or Mullice. We have held that “[t]he mere fact that [some witnesses’] sentences were later altered is not evidence that a deal existed prior to their testimony at trial.” Williams v. Coyle, 260 F.3d 684, 707 (6th Cir.2001); see also Matthews v. Ishee, 486 F.3d 883, 896 (6th Cir.2007). Accordingly, the fact that both Nunn and Mullice were not prosecuted for particular crimes, without more, is insufficient, under our precedents, to establish that an undisclosed deal existed.
Even assuming that there was an undisclosed agreement with Nunn, the additional impeachment evidence would not be prejudicial, because the jury was made aware that Nunn was admitting in open court to criminal acts, but stated he did not expect to be prosecuted. Nunn testified at trial that he did not have an agreement with anyone from the state or federal prosecutor’s office regarding any benefit he would receive for his testimony. R. 334 (Trial Tr. at 3437) (Page ID #4540). However, on cross-examination, Nunn also stated that he knew the government could *553charge him with the crimes he admitted to under oath, and that if he was prosecuted for those crimes, he could be facing “a substantial amount of time up to probably life in prison.” Id. at 3486 (Page ID # 4589). Nunn was cross-examined thoroughly on his motives for testifying, and the improbability of his providing testimony regarding his own criminal activities without a written plea agreement, without a lawyer present, and with no promise of immunity. See id. at 3486-87 (Page ID #4589-90). Nunn also admitted to the jury that he was a liar and a thief. Id. at 3490 (Page ID # 4593). As in Akrawi, the cross-examination of Nunn “would arguably have been more effective if evidence of the mutual understanding [with the prosecutor] had been disclosed prior to trial, but only incrementally so.” 572 F.3d at 264. Accordingly, the non-disclosure of a tacit agreement between Convertino and Nunn, assuming an agreement existed, was not prejudicial.
Mulliee similarly denied receiving benefits from the government for his testimony. R. 331 (Trial Tr. at 2780) (Page ID # 6762). However, Mulliee admitted to the jury that he had pending charges against him for possession of crack cocaine (and that he was guilty of those offenses), but that he did not expect the government to pursue the case against him. However, on cross-examination, he could not come up with an answer for why he did not expect to be charged or prosecuted for these crimes. Id. at 2782-86 (Page ID # 6764-68). The jury understood that Mulliee had a motive to testify favorably for the government and that he may have stood to benefit significantly through his cooperation. Thus, any undisclosed impeachment evidence would have been cumulative. Accordingly, even if Convertino suppressed evidence of deals with Nunn and Mulliee, the additional impeachment evidence would not “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. We hold that Jefferson’s Brady claims relating to Nunn and Mulliee fail.
3. Eva Taylor
Like Warren, Palmer, and Alexander, Taylor was cross-examined about her plea agreement with the government. She admitted that, absent her cooperation with the government, she would face a mandatory minimum of ten years in prison and would likely receive a sentence of between twenty-five and thirty years in prison. R. 322 (Trial Tr. at 1472) (Page ID # 7087). However, pursuant to her plea agreement, if Taylor cooperated with the government and testified against her coconspirators, the government would make a recommendation to the sentencing judge that she receive a sentence of only four years. Id. at 1473 (Page ID # 7088). Taylor also admitted lying to the government in the past. See id. at 1416 (Page ID # 7031). After Jefferson’s trial ended, Taylor ultimately was sentenced to only two years of probation. Assuming there was an undisclosed deal, as the circumstantial evidence of Taylor’s grossly reduced sentence suggests, the cross-examination repeated above demonstrates that Taylor’s credibility was impeached thoroughly regarding her incentives to testify favorably towards the government. Accordingly, the undisclosed evidence would be cumulative and not prejudicial.
4. Aaron Bowles
Like Jefferson’s Brady claims with respect to the trial witnesses, Jefferson’s Brady claim regarding an undisclosed promise with Aaron Bowles (“Bowles”) in exchange for his testimony at sentencing fails, because even if such an undisclosed promise existed, it would not *554meet the standard for prejudice.4 On cross-examination, Bowles admitted that he was cooperating with the government so that it would make a recommendation for a reduction in his sentence. R. 423-1 (Sent. Hr’g Tr. at 64-65) (Page ID # 3128-29). Accordingly, Bowles’s credibility was impeached, because it was established that he had a strong motive to testify to the government’s satisfaction.
More significantly, the primary basis for the district court’s drug-quantity determination was Jefferson’s admissions to law enforcement officers when he was initially arrested. See R. 425 (Sent. Hr’g Tr. at 23-24) (Page ID # 3171-72). Jefferson conceded that if his statement to law enforcement officers was considered reliable evidence, it would establish that he was responsible for three-and-a-half kilograms of cocaine. R. 285 (Defi’s Supp. Sent. Mem. at 3) (Page ID # 9849). The district court found this statement reliable, and thus found that Jefferson was responsible for at least one-and-a-half kilograms of cocaine. R. 425 (Sent. Hr’g Tr. at 23-24) (Page ID #3171-72). Although the district court also credited Bowles’s testimony, even with additional impeachment evidence, there is not a reasonable probability that the district court would have found Jefferson liable for less than one-and-a-half kilograms of cocaine. Thus, Jefferson’s claim relating to Bowles fails.
5. Donald Bailey
Jefferson’s assertions regarding Officer Donald Bailey (“Bailey) lack merit. Jefferson asserts that Convertino withheld information regarding Bailey’s disciplinary history from the court, or otherwise lied about that history. Appellant Br. at 41-42. However, the trial transcript indicates that defense counsel was aware of the information, and that Convertino did not deny it, but only objected to the questioning on evidentiary grounds. R. 319 (Trial Tr. at 907-17) (Page ID # 5259-69). Jefferson has not established that Convertino withheld any information from defense counsel relating to Bailey’s conduct in unrelated state-court cases.
Although the record in this ease suggests egregious prosecutorial misconduct, the bad faith of the prosecutor does not impact our Brady analysis. See Strickler, 527 U.S. at 288, 119 S.Ct. 1936 (“ ‘If the suppression of evidence results in constitutional error, it is because of the character of the evidence, not the character of the prosecutor.’ ” (quoting United States v. Agurs, 427 U.S. 97, 110, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976))). We affirm the district court’s conclusion that Jefferson’s Brady claims fail on the merits.
III. CONCLUSION
For the foregoing reasons, we AFFIRM the judgment of the district court.