OPINION
SILER, Circuit Judge.In 1987, Abu-Mi Abdur’Rahman was convicted of first-degree murder, assault with intent to commit first-degree murder, and armed robbery. He now appeals the district court’s denial of relief on his Rule 60(b) motion. For the following reasons, we AFFIRM.
BACKGROUND
On February 16, 1986, Abdur’Rahman purchased marijuana from Patrick Daniels and Norma Norman at the couple’s shared apartment in Nashville, Tennessee.1 This purchase prompted Abdur’Rahman and his accomplice, Harold Devalle Miller, to plan to rob Daniels and Norman. On February 17, Abdur’Rahman, armed with a shotgun, and Miller, armed with an unloaded pistol, went to Daniels’s apartment under the pretense of making another drug purchase. Brandishing their weapons once inside, Abdur’Rahman and Miller bound Daniels and Norman with duct tape, and took Daniels’s bank card, $300 in cash, and marijuana. Abdur’Rahman informed Daniels that he had been sent from Chicago to “clean up everything” and that he was there to teach Daniels a lesson. Abdur’Rahman then took a butcher knife from the kitchen and stabbed Daniels six times in the chest. He also stabbed Norman several times in the back before he and Miller fled. Daniels died from his wounds, but Norman survived.
A jury convicted Abdur’Rahman of murder, assault with intent to commit first-degree murder, and armed robbery. At sentencing, Abdur’Rahman testified that he was encouraged to commit the robbery by a “quasi-religious paramilitary group” called the Southeastern Gospel Ministry (“SEGM”). He stated that the goal of the SEGM was to “cleanse the black community of drug dealers and other undesirable elements.” He also testified that Allen Boyd, a leader within the SEGM, furnished the shotgun he used during the crime, and aided him and Miller after-wards. Abdur’Rahman received the death penalty for his murder conviction and two consecutive life terms for each of his other convictions. The Tennessee Supreme Court affirmed Abdur’Rahman’s convictions and sentences, see State v. Jones, 789 S.W.2d 545 (Tenn.1990), and he unsuccessfully pursued state post-conviction relief, see Jones v. State, No. 01 C01-9402-CR00079, 1995 WL 75427, at * 1-3 (Tenn. Crim.App. Feb. 23, 1995).
Abdur’Rahman filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254. Abdur’Rahman v. Bell, 999 F.Supp. 1073 (M.D.Tenn.1998). The district court granted relief, but we reversed and vacated the judgment. Abdur’Rahman, 226 F.3d at 708-09. Abdur’Rahman then filed a motion for relief under Rule 60(b). See Abdur’Rahman v. Bell, No. 3:96-0380, 2001 WL 1782874, at *1 (M.D.Tenn. Nov. 27, 2001). After several appeals, the district court granted Abdur’Rahman’s motion to consider the merit of certain claims that it earlier concluded were procedurally defaulted in Abdur’Rahman’s initial § 2254 petition. Abdur’Rahman v. Bell, No. 3:96:0380, 2009 WL 211133 (M.D.Tenn. Jan. 26, 2009).
*472Among his several claims for relief, Abdur’Rahman argued that the prosecution withheld two pieces of evidence before sentencing, in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963): pretrial statements made by Miller regarding the influence of the SEGM on the crime, and Detective Mark Garafola’s account of Abdur’Rahman’s self-destructive behavior while in police custody. With this withheld evidence, Abdur’Rahman argues that one or more jurors could have concluded that a term of life imprisonment rather than death was a more appropriate sentence in his case. The district court, however, denied relief. It held that the prosecution’s suppression of Miller’s pre-trial statements did not violate Brady, either because Abdur’Rahman already knew of this information or because the evidence was not material. Abdur’Rahman, 2009 WL 211133, at *7. It also held that Detective Garafola’s report was not material. Id. at *9-10. We granted Abdur’Rahman a certificate of appealability (COA) to consider whether the district court properly rejected these two Brady subclaims.
DISCUSSION
A. Standard of Review
We review a district court’s denial of a petitioner’s habeas claims de novo. Joseph v. Coyle, 469 F.3d 441, 449 (6th Cir.2006). Factual findings made by the district court are reviewed for clear error, but mixed questions of law and fact are reviewed de novo. Boykin v. Webb, 541 F.3d 638, 642 (6th Cir.2008).
Abdur’Rahman filed his § 2254 habeas petition on April 23, 1996- — one day before the effective date of the Antiterrorism and Effective Death Penalty Act. As a result, the pre-AEDPA standard of review applies here. See Coleman v. Mitchell, 268 F.3d 417, 427 (6th Cir.2001) (citing Mapes v. Coyle, 171 F.3d 408, 413 (6th Cir.1999)). Thus, we presume the correctness of state court factual findings, which are rebuttable only by clear and convincing evidence. Id. We review determinations of law, or determinations involving mixed questions of law and fact, de novo. Id. Because Abdur’Rahman’s appeal was brought after AEDPA’s effective date, however, AEDPA’s requirement that he secure a COA still applies. See Mackey v. Dutton, 217 F.3d 399, 406-07 (6th Cir. 2000).
B. Abdur’Rahman’s Cumulative Error Arguments
In addition to his individual Brady claims, Abdur’Rahman argues that these claims should be cumulated with the prosecutorial misconduct or Strickland claims he raised in his initial § 2254 petition. Even if these errors do not deny him due process when considered in isolation, Abdur’Rahman argues that the prejudice resulting from either cumulation makes his death-sentence unfair.
Because Abdur’Rahman raised these cumulative error arguments for the first time on habeas review, we may not consider them here. He suggests that we follow Derden v. McNeel, 978 F.2d 1453, 1456-57 (5th Cir.1992), where an en banc Fifth Circuit permitted a habeas petitioner to raise a cumulative error argument without first making that argument before the state court below. Under our own circuit’s precedent, however, cumulative error arguments must be raised separately in the state court and are subject to procedural default on habeas review. See Keith v. Mitchell, 455 F.3d 662, 679 (6th Cir.2006) (citing Lorraine v. Coyle, 291 F.3d 416, 447 (6th Cir.2002)). Abdur’Rahman failed to raise these cumulative error claims on direct appeal or during post-conviction relief *473in state court. Instead, he only raised a generalized cumulative error argument for the first time in his habeas petition. Because we are bound by this circuit’s prior precedents, see Sandusky Mall Co. v. N.L.R.B., 242 F.3d 682, 692 (6th Cir.2001), Abdur’Rahman cannot raise either cumulative error argument here.
Review of his cumulative error arguments is also foreclosed because the COA does not certify the claims for appeal. A COA is a “jurisdictional prerequisite” to the consideration of the merits of an appellant’s habeas claims, see Miller-El v. Cockrell, 537 U.S. 322, 336, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003), and we may not consider claims not certified for appeal, see 28 U.S.C. § 2253(c); Seymour v. Walker, 224 F.3d 542, 561 (6th Cir.2000). Here, the COA allows Abdur’Rahman to appeal the denial of two Brady subclaims and permits him to make “cumulative-effect arguments” regarding only those Brady sub-claims, “even if it involves referring to factual allegations that underpin prosecutorial-misconduct subclaims.” (emphasis added). As we explain more fully in Part C-2 below, this language acknowledges the general rule that we consider Brady materiality collectively, rather than looking at each suppressed item in isolation. It does not permit Abdur’Rahman to make cumulative-effect arguments regarding claims based on distinct legal theories. Because we treat cumulative error arguments as separate claims, and Abdur’Rahman’s cumulative error arguments are not included within the COA, we cannot consider them here.
C. Brady Claims
Abdur’Rahman argues that the prosecution violated Brady by withholding two pieces of evidence: Miller’s pre-trial statements explaining the influence of the SEGM over their crime, and Detective Garafola’s police report describing Abdur’Rahman’s self-destructive behavior at the time of his arrest.
“[T]he suppression by the prosecution of evidence favorable to an accused ... violates due process where the evidence is material either to guilt or to punishment.” Bell v. Bell, 512 F.3d 223, 231 (6th Cir.2008) (en banc) (quoting Brady, 373 U.S. at 87, 83 S.Ct. 1194). A successful Brady claim requires the defendant to demonstrate that: (1) the evidence in question was favorable to him; (2) the prosecution suppressed the relevant evidence, either purposefully or inadvertently; and (3) the state’s actions resulted in prejudice. Id. (citing Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)). This rule applies to evidence that is exculpatory in nature as well as evidence that a defendant could use to impeach a government witness. See United States v. Bagley, 473 U.S. 667, 676-77, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).
1. Miller’s Pre-Trial Statements about the SEGM
Abdur’Rahman’s first Brady claim concerns pre-trial statements that Miller made to the prosecution concerning the SEGM’s role in his murder of Daniels. No contemporaneous record of these statements exists. Rather, Ross Aider-man, Miller’s state trial counsel, testified that Miller made pre-trial statements to the prosecution that conflicted with his eventual testimony at Abdur’Rahman’s trial. Abdur’Rahman derives the substance of Miller’s pre-trial statements from Miller’s testimony at a post-conviction hearing and at Miller’s sentencing hearing, and alleges that Miller said the following:
(1) The purpose of the SEGM was to rid the community of drug dealers; (2) the “sole” purpose of going to Daniels’s apartment was to effect the SEGM’s plan to *474stop drug dealing in the community; (3) William Beard, a leader within the SEGM, provided Miller with the pistol he used to rob Daniels, and Abdur’Rahman said he had obtained the shotgun used in the crime from Alan Boyd; (4) Abdur’Rahman made a phone call after the offense, and Boyd arrived at Miller’s apartment a short time later; (5) Miller overheard a conversation between Boyd and Abdur’Rahman at his apartment after the offense in which Boyd told Abdur’Rahman something like “just be cool, go back to work”; and (6) Beard gave Miller money before he fled the state, and Miller misled Beard about his getaway because he feared what Boyd and Beard might do.
Abdur’Rahman argues that the district court erred because the prosecution never informed him before sentencing that Miller made these statements. At trial, Miller stated that the robbery was Abdur’Rahman’s idea and was committed for the purpose of stealing drugs. At the sentencing phase of the trial, Abdur’Rahman explained that he was influenced by the SEGM to rob Daniels, but the prosecution called this explanation “bunk.” Abdur’Rahman argues that Miller’s pre-trial statements could have been used at the sentencing phase not only to corroborate his own testimony that the SEGM influenced him to go to Daniels’s apartment and attempt the robbery, but also to discredit Miller’s testimony that Abdur’Rahman masterminded the crime.2
Because, at the time of the trial, Abdur’Rahman knew about the SEGM and knew that Miller had discussed the SEGM with the prosecution before trial, the district court correctly held, that withholding Miller’s pre-trial statements did not violate Brady. The Brady rule “only applies to evidence that was known to the prosecution, but unknown to the defense, at the time of trial.” Apanovitch v. Houk, 466 F.3d 460, 474 (6th Cir.2006). “No Brady violation exists where a defendant knew or should have known the essential facts permitting him to take advantage of any exculpatory information,” United States v. Clark, 928 F.2d 733, 738 (6th Cir.1991) (per curiam) (internal citations and quotation marks omitted), and this principle applies equally in the impeachment context, see Byrd v. Collins, 209 F.3d 486, 517 (6th Cir.2000). Where the defense is provided with enough information to enable counsel to impeach a witness, withholding that witness’s statements does not violate Brady. Id. Ultimately, where the alleged Brady evidence is available to the defense, “there is really nothing for the government to disclose.” Bell, 512 F.3d at 235 (quoting Coe v. Bell, 161 F.3d 320, 344 (6th Cir.1998)).
Here, Abdur’Rahman knew the essential facts reflected in Miller’s pre-trial statements before the sentencing phase. In fact, Abdur’Rahman’s testimony repeated the substance of Miller’s pre-trial statements, and Abdur’Rahman decided not to call Miller as a witness for this very reason. Abdur’Rahman testified that he and Miller were both members of the SEGM, that its purpose was to rid the black community of drug dealers, and that Beard and Boyd were leaders within the SEGM. Abdur’Rahman, 2009 WL 211133, at *7. He also testified that Boyd and Beard provided the weapons used during the of~ *475fense, and that Boyd helped Miller escape afterwards. Id.; see Abdur’Rahman, 226 F.3d at 699. Abdur’Rahman did not testify that the SEGM’s mission was the “sole” motive for the crime — in fact, he contradicted this, denying that the SEGM had turned him into a murderer or that other members of the SEGM were involved in the crime. Id. But his testimony did reveal that the SEGM provided some influence. He stated that members of the SEGM had explained how to confront drug dealers and suggested that they might be blackmailed for money. Id. Because Abdur’Rahman already knew of the exculpatory information in Miller’s statements, there was little remaining for the prosecution to disclose.
Nor does the impeachment value of Miller’s pre-trial statements require that we reverse the district court’s holding. Abdur’Rahman argues that the ultimate value of the withheld statements is not what was said, but rather that Miller said them. Abdur’Rahman, however, knew that Miller had discussed the SEGM with the prosecution before trial. Abdur’Rahman’s trial counsel wrote a letter to the prosecution before the sentencing phase, acknowledging that Miller “ha[d] advised your office of the existence of [the SEGM].” The prosecution confirmed Abdur’Rahman’s understanding, stating that it had learned about the SEGM through its conversations with Miller. Given what Abdur’Rahman already knew about the SEGM and its influence, the prosecution’s acknowledgment that Miller discussed the SEGM with it before trial provided Abdur’Rahman sufficient information to enable him to impeach the credibility of Miller’s testimony at trial. Abdur’Rahman’s decision not to do so was not the fault of the prosecution. See Byrd, 209 F.3d at 517. Accordingly, the district court did not err in concluding that the prosecution’s nondisclosure of Miller’s pre-trial statements did not violate Brady.3
2. Abdur’Rahman’s Head Banging upon Arrest
Abdur’Rahman’s second Brady claim concerns Detective Garafola’s report detailing his conduct upon arrest. On February 19, 1986, whén Abdur’Rahman was arrested for murdering Daniels, Detective Garafola authored a report that read, in part:
When we returned to our office Det Elmore and myself attempted to interview [Abdur’Rahman]. He was in an interview room and when we entered the room [Abdur’Rahman] was crying. He would not respond to our questions. The only statement he made was “I only killed one man in my life and that was because he was trying to fuck me.” He then started to hit his head on the table and then he jumped up still handcuffed to the chair and banged his head up against the wall. We got him under control and then took him to the booking room. In the booking room he started to bang his head on the wall again. Det Elmore was able to control him. We took Polaroid pictures of him and also mug shots with his glasses on and off.
The government concedes that this portion of Detective Garafola’s report was redacted and not shown to Abdur’Rahman at trial or before sentencing. Abdur’Rahman *476argues that this report could have been used to show that he was “seriously mentally ill when he was arrested” and that he had been mentally ill for decades. He also argues this evidence would have demonstrated that he was particularly susceptible to manipulation by the SEGM, disproving the prosecution’s characterization of him as a depraved killer. The mitigative effect of Detective Garafola’s report, he argues, would have caused one or more jurors to vote in favor of a life sentence.
As an initial matter, we are not convinced that, at the time of the sentencing phase, Abdur’Rahman did not know the essential facts of the behavior described in Detective Garafola’s report. Although it is possible that Abdur’Rahman was not personally aware of his own head-banging, his trial counsel indicated that “something happened at the time [Abdur’Rahman] was arrested and he might have been put in a padded cell if he maybe lost his temper or something of that nature.” Trial counsel interviewed Detective Garafola and “talked about what happened at the point of arrest.” Moreover, a Davidson County Sheriffs Department incident report indicated that, four hours after his interview with Detective Garafola, “[Abdur’Rahman] started beating his head against the floor.” Abdur’Rahman has never claimed that this report was suppressed; apparently, however, his trial counsel apparently never took steps to obtain it. If Abdur’Rahman’s counsel did not know the essential facts of Abdur’Rahman’s head-banging as described by Detective Garafola, he likely should have discovered them through further investigation.
Because the prosecution’s suppression of this part of Detective Garafola’s report does not undermine our confidence in Abdur’Rahman’s sentence, the district court did not err in rejecting the second Brady claim. A failure to disclose evidence favorable to the defense is “ ‘material,’ and therefore ‘prejudicial,’ 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.’ ” Apanovitch, 466 F.3d at 475 (quoting Strickler, 527 U.S. at 280, 119 S.Ct. 1936). This “reasonable probability” exists when the government’s suppression of evidence undermines confidence in the outcome of the trial. Id. (citing Kyles v. Whitley, 514 U.S. 419, 434, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995)). Here, because Tennessee’s capital sentencing law requires a unanimous jury vote to impose a death sentence, see TenmCode Ann. § 39-2-203(h) (1983), the relevant inquiry is “whether there is a reasonable probability that the withheld evidence would have altered at least one juror’s assessment of the appropriate penalty for [Abdur’Rahman’s] crime,” Cone v. Bell, 556 U.S. 449, -, 129 S.Ct. 1769, 1773, 173 L.Ed.2d 701 (2009).
To determine whether the nondisclosure of Detective Garafola’s report was material, Abdur’Rahman urges us to also consider the prejudice arising from his first Brady claim along with that arising from “the prosecutor’s further misconduct” — in particular, the presentation of his “prejudicial” indictments at sentencing and the suppression of a transcript from his 1972 murder trial. His request is over-broad. When granting a COA in this case, we “permitted [Abdur’Rahman] to make cumulative-effect arguments with respect to the subclaims on which [the COA was granted], even it if involves referring to the factual allegations that underpin prosecutorial-misconduct subclaims on which [the COA was denied].” In so stating, we merely acknowledged the well-established rule that, when considering the materiality of alleged Brady evidence, we consider the cumulative effect of all of the undisclosed *477evidence, rather than each item in isolation. See Doan v. Carter, 548 F.3d 449, 460 (6th Cir.2008) (citing Kyles, 514 U.S. at 436, 115 S.Ct. 1555). Accordingly, our cumulative effect analysis looks only to other evidence that was both suppressed and exculpatory. Cf. Smith v. Sec’y, Dep’t of Corr., 572 F.3d 1327, 1348 (11th Cir. 2009) (cumulating the effect of only those Brady claims “that do involve favorable evidence that was actually suppressed ”) (emphasis added). Because Brady does not apply to Miller’s pre-trial statements, as they were not “undisclosed,” we will not consider their potential impact when determining the materiality of the redacted portion of Detective Garafola’s report. Given that we did not grant a COA on Abdur’Rahman’s other claims, and therefore do not review the merits of those claims here, the only evidence that we may consider for cumulative effect is the 1972 murder trial transcript. See Abdur’Rahman, 999 F.Supp. at 1089-90 (holding that 1972 murder trial transcript was suppressed and exculpatory, but not material).
In analyzing materiality, we begin by looking at any prejudice arising from the suppression of part of Detective Garafola’s report. Had it been admitted in its entirety, it would have done little to establish Abdur’Rahman’s mental illness at the time of the offense or before. Abdur’Rahman was evaluated at the time of trial and found not to be incompetent or insane. As evidence of mental illness, Detective Garafola’s report is far from conclusive. Head banging like Abdur’Rahman’s could be a manifestation of many things (including frustration, anger, sadness, or mental illness) and therefore, in and of itself, is hardly dispositive of mental illness. Placing Abdur’Rahman in a padded cell is no more conclusive, and only represents the decision of law enforcement, not a mental health expert, that Abdur’Rahman was a potential danger to himself. The only other corroborating evidence of mental illness that Abdur’Rahman presented at sentencing was the testimony of himself and his wife. The addition of Detective Garafola’s report adds little to Abdur’Rahman’s narrative that he was mentally ill, and had it been presented, the prosecution could have rebutted it with considerable expert testimony to the contrary.
Nor would admission of Detective Garafola’s report have disproved the prosecution’s narrative characterizing Abdur’Rahman as a depraved killer. Abdur’Rahman’s head banging, under the circumstances described above, does not contradict the prosecution’s description of Abdur’Rahman as “not someone suffering from several emotional disturbance.” Further, because Abdur’Rahman testified to the contrary at his sentencing phase, Detective Garafola’s report does little to establish that Abdur’Rahman was susceptible to manipulation by the SEGM. Abdur’Rahman testified that the SEGM did not turn him into a murderer, and that Beard and Boyd were not involved in the crime. Abdur’Rahman, 2009 WL 211133, at *7. It is not likely that Detective Garafola’s report would have changed the jury’s impression of Abdur’Rahman.
In fact, based on Detective Garafola’s report alone, the jury could just as easily have viewed Abdur’Rahman’s head banging as evidence of his culpability rather than as mitigation. Abdur’Rahman had already been convicted of a prior murder at the time of his arrest and was now accused of stabbing another man to death. Once in custody, Abdur’Rahman surely knew that he faced either a death sentence or life in prison. Rather than mental illness, then, the jury could have viewed Abdur’Rahman’s head banging as evidence of guilt, distress or frustration that under*478scored the danger he posed to himself and to others. As a result, while the redacted portion of Detective Garafola’s report might have been favorable to Abdur’Rahman, it is highly unlikely that its admission at sentencing would have caused any juror to alter his assessment that Abdur’Rahman deserved the death penalty.
Our conclusion remains unchanged, even when considering materiality in light of any prejudice arising from the suppression of the 1972 murder trial transcript. As the district court noted in an earlier phase of Abdur’Rahman’s habeas proceedings, any prejudice arising from the suppression of that evidence was immaterial. See Abdur’Rahman, 999 F.Supp. at 1089-90. When that item is considered together with the redacted portions of Detective Garafola’s report, the prospect of prejudice is no more convincing. Although both items allegedly relate to Abdur’Rahman’s mental health history, neither is especially strong evidence, and the combined effect of them by no means tends to “put the whole case in a different light as to undermine confidence in the verdict.” See Cone, 129 S.Ct. at 1783 (internal quotation marks omitted); cf. Poindexter v. Mitchell, 454 F.3d 564, 573 (6th Cir.2006) (“[Wjhere one is left with pure speculation on whether the outcome of the trial could have been any different, there is an insufficient showing of prejudice[.]” (internal quotation marks, citation, and alteration in original omitted)).
AFFIRMED.
. The facts underlying Abdur'Rahman's Tennessee convictions are derived from this court’s review of his first habeas appeal, see Abdur’Rahman v. Bell, 226 F.3d 696, 699 (6th Cir.2000).
. As the warden notes, Abdur'Rahman argued in his petition for a writ of habeas corpus that the prosecution’s suppression of Miller’s statements was wrongful only because the statements contained exculpatory information. Abdur’Rahman did not argue that the statements would have impeached Miller’s trial testimony. While Abdur’Rahman may have waived this particular argument for purposes of appeal, see Barker v. Shalala, 40 F.3d 789, 793-94 (6th Cir.1994), we nevertheless consider it here.
. The dissent suggests our analysis on this point is flawed because we erroneously presume Abdur’Rahman's trial counsel was competent. While we did acknowledge Abdur’Rahman's counsel was ineffective in failing to investigate his background and mental health history, see Abdur’Rahman, 226 F.3d at 708, this does not compel that we presume his counsel was also ineffective in failing to discover the details of Miller’s testimony or to cross-examine him about it.