
540 F.3d 623 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
James ERVIN and Jay Zambrana, Defendants-Appellants.
Nos. 05-4700, 06-1834.
United States Court of Appeals, Seventh Circuit.
Argued January 14, 2008.
Decided September 2, 2008.
*624 Daniel L. Bella (argued), Office of the United States Attorney, Hammond, IN, for Plaintiff-Appellee.
Jerold S. Solovy, Benjamin J. Bradford (argued), Jenner & Block, Chicago, IL, for James Ervin Defendant-Appellant.
Benjamin J. Bradford, Jenner & Block, Chicago, IL, Christopher W. Zibart, Michael S. Baig (argued), Foley & Lardner, Chicago, IL, for Jay Zambrana Defendant-Appellant.
Before POSNER, KANNE, and WILLIAMS, Circuit Judges.
KANNE, Circuit Judge.
A federal grand jury charged Jay Zambrana and James Ervin with violating numerous provisions of federal law by participating in a drug-trafficking conspiracy, see 18 U.S.C. §§ 2, 922(g)(1), 1951, 1956(a)(1)(A)(i), (a)(1)(B)(i), 1957; 21 U.S.C. §§ 841(a)(1), 843(b), 846, 856(a)(1), and by killing two men in furtherance of that conspiracy, see 18 U.S.C. § 2; 21 U.S.C. § 848(e)(1)(A). Before trial, Zambrana sought to sever the homicide counts from the drug-conspiracy counts, see Fed. R.Crim.P. 14(a), to no avail. A jury found Zambrana and Ervin guilty on all counts, based largely on the extensive testimony of the two men's co-conspirators who agreed to testify against them in exchange for immunity or reduced sentences. Two years later, Zambrana and Ervin filed motions seeking a new trial, see Fed. R.Crim.P. 33(a), on the grounds that new evidence came to light showing that (1) one of the co-conspirators who testified against them engaged in several acts of misconduct *625 while detained at the city jail in Hammond, Indiana, before trial; and (2) the government withheld the evidence of that misconduct in derogation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). The district court denied the motions. We affirm.

I. HISTORY
In September 1997, officers with the police department in Lake County, Indiana, arrested Alvestia McKeller in Merrillville, Indiana, after they recovered one kilogram of cocaine from his car's trunk during a traffic stop. McKeller quickly informed the officers that he had purchased the cocaine from his cousin, who had, in turn, obtained the drugs from Zambrana. McKeller's admissions spurred a wide-scale investigation of Zambrana by the Drug Enforcement Administration; the Internal Revenue Service; the Bureau of Alcohol, Tobacco, Firearms, and Explosives; and the Federal Bureau of Investigation (FBI). That investigation culminated in 2002 with the filing of a 40-count indictment against Zambrana, Ervin, and seven others; Zambrana was a named defendant in 29 of the counts, and Ervin was named in eleven.
In general, the indictment alleged that the nine men comprised a wide-reaching drug-trafficking ring in northwest Indiana, and that as part of the conspiracy they obtained and distributed marijuana, heroin, and cocaine; extorted others; laundered money to conceal the conspiracy; carried and used firearms to further the conspiracy; and committed numerous violent actsincluding murderto supply the conspiracy with money and drugs. As pertinent here, the indictment claimed that Zambrana led the drug-trafficking ring, and that Ervinan officer with the police department in Gary, Indianaacted as his muscle. As part of his leadership duties, the indictment continued, Zambrana would launder the revenue derived from the conspiracy by visiting riverboat casinos, gambling with the drug money, and exchanging his "winnings" for "clean" cashier's checks from the casinos. Finally, the indictment alleged that Zambrana, Ervin, and two others conspired to kill Raul Hurtado and Gil Nevarez as part of a scheme to obtain five kilograms of cocaine.
About six months before trial, Zambrana filed a motion to sever the indictment's homicide counts from the drug-conspiracy counts. In his motion, Zambrana asserted that he "wish[ed] to testify" in his own defense against the homicide counts, but "[t]hat combining all the counts at one trial" would prevent him from doing so if he chose to exercise his right not to testify as to the drug-conspiracy counts. Moreover, Zambrana argued, trying the homicide and drug-conspiracy counts together would prevent him from receiving a fair trial. Zambrana simultaneously filed a notice of affirmative defense, in which he stated that he "may rely on [an] alibi defense" to respond to the homicide charges. See Fed.R.Crim.P. 12.1(a)(1)-(2). Zambrana contended that he "was gambling on the casino boats" during the time that the government had alleged that Hurtado's and Nevarez's murders occurred, and explained that he would "rely on records provided by the [g]overnment to establish such alibi." The district court rejected Zambrana's arguments, concluding that he neither provided "any specific testimony he intend[ed] to give" regarding the homicide counts, nor explained how a single trial on all the counts in the indictment would prevent the jury from reaching a reliable verdict. The court therefore denied his motion to sever.
The case proceeded to trial, and the government presented 57 witnesses, including five of Zambrana's and Ervin's co-conspirators *626 who described the inner-workings of the drug-trafficking ring. As relevant to this appeal, three of Zambrana's and Ervin's cohortsCarlos Ripoll, Denny Arreola, and Tony Clintonexplained how Zambrana and Ervin participated in the conspiracy, and described Zambrana's and Ervin's roles in the murder of Hurtado and Nevarez.
In a nutshell, Ripoll, Arreola, and Clinton together testified that (1) Zambrana approved of Ripoll's and Arreola's plan to rob Hurtado and Nevarez of their cocaine and murder them; (2) Zambrana ordered Ervin to coordinate and to execute the heist and killings; (3) in accordance with the plan, Ervin "arrested" Hurtado and Nevarez during a sham traffic stop, took their cocaine, and drove the two men to the Puerto Rican Benefica Club in Gary; (4) at the Benefica Club, Arreola witnessed Ervin and another co-conspirator, Gabriel Benavides, strangle Hurtado and Nevarez; (5) Zambrana ordered Clinton to help Ervin dispose of the bodies; (6) Clinton helped Ervin load the bodies into the trunk of a car, followed him in another car as they drove to the south side of Chicago, Illinois, and watched as Ervin set the car on fire in a secluded alley (where the Chicago Fire Department would later find it and the two bodies it contained); and (7) on the return trip to Gary, Ervin described in graphic detail to Clinton how he and Benavides strangled Hurtado and Nevarez.
Zambrana's and Ervin's attorneys thoroughly impeached Ripoll's, Arreola's, and Clinton's testimony. The defense asked pointed questions to each man about how he was originally charged with participating in the drug-trafficking conspiracy, and forced the men to admit that they agreed to testify against Zambrana and Ervin only after the government offered them immunity from the homicide counts or reduced sentences as to the drug-conspiracy counts. Arreola, in particular, was questioned further about his role in Hurtado's and Nevarez's robbery and murders, and was forced to admit that he had lied to the police when they first interviewed him about the crime. The defense also got the three men to admit that they had several opportunities to communicate with each other after they had agreed to testify against Zambrana and Ervin; Arreola similarly admitted that while he was housed in the Metropolitan Correctional Center ("MCC") in Chicago during trial, a guard smuggled a cell phone to him, and that he used the phone to make unmonitored telephone calls. The defense also questioned Arreola about his membership in the notorious Latin Kings street gang. And in their continuing effort to impeach Arreola, the defense called a character witness to testify that Arreola was untrustworthy and had a reputation for stealing, and also called an inmate at the MCC who claimed that, while Arreola was detained there, he had stated that Zambrana had nothing to do with the murders. Arreola's credibility was further attacked in the defense's closing arguments.
Before the jury retired to deliberate, the district court carefully instructed it on how to weigh the evidence regarding the many crimes alleged. Specifically, the court informed the jury that "[e]ach count of the [i]ndictment charge[d] each defendant named in that count with having committed a separate offense"; stated that the jury "must give separate consideration both to each count and to each defendant"; and ordered the jury to "consider each count and the evidence relating to it separate and apart from every other count." The jury then entered into its deliberations, and subsequently found Zambrana and Ervin guilty on all counts.
*627 Both Zambrana and Ervin remained in custody awaiting sentencing for over two years. But then in November 2005, the United States Attorney's Office sent a letter to Zambrana's and Ervin's attorneys, stating that it had recently learned that while Arreola was detained at the Hammond City Jail before trial, he engaged in various incidents of misconduct with some of the jail's personnel. The letter stated that, among other things, Arreola had been permitted to smoke cigarettes in the jail garage area unsupervised, to have sexual intercourse with female visitors, to make unmonitored telephone calls, and to receive visits at the jail without first placing his visitors on the jail's visitors log. The letter also detailed that Arreola had a "personal relationship" with a female guard, and that other guards had thrown a birthday party for Arreola's girlfriend, had purchased food for him, and had allowed visitors to give him Xanax. Nevertheless, the letter emphasized that the United States Attorney's Office and "the federal investigators involved with the Jay Zambrana prosecution and trial" were not aware of the misconduct before the trial. Instead, the letter continued, the Office had learned of the misconduct only after an investigation undertaken by the United States Marshals and the FBI confirmed that the misconduct had, in fact, occurred; that investigation, the letter stated, had been completed just "recently."
Ervin filed a motion for new trial shortly after receiving the United States Attorney's letter. Ervin contended that the newly discovered evidence of Arreola's misconduct at the Hammond City Jail warranted a new trial so he could use the information to impeach Arreola. Ervin also alleged that the government had been aware of Arreola's misconduct before trial, and thus contravened Brady by suppressing the evidence of that malfeasance. Ervin did not, however, request an evidentiary hearing on his motion, and instead went forward with sentencing. And at his sentencing hearing, Ervin accepted the government's representations regarding both Arreola's misconduct and its lack of knowledge of the misconduct, but contended that the revelations nevertheless justified a new trial.
The district court rejected Ervin's arguments, concluding that the evidence of Arreola's misconduct did not warrant a new trial as newly discovered impeachment evidence because, among other things, Arreola already had been thoroughly impeached. Moreover, the court continued, Ervin failed to show that the government suppressed the evidence of Arreola's malfeasance: "There was no evidence offered that any [federal] agency knew of the violations taking place at the Hammond City Jail or that it should have been known by the prosecutors." And even if the government had suppressed the evidence of Arreola's misconduct, the court continued, the suppression could not have run counter to Brady because the evidence was merely cumulative impeachment evidence. The court thus denied Ervin's motion and sentenced him to life imprisonment.
Zambrana also filed a motion for new trial, mostly echoing the newly discovered evidence and Brady arguments put forward by Ervin, and further asserting that the government withheld evidence showing that Ripoll, Arreola, and Clinton discussed their testimony before trial as part of a greater plan to frame Zambrana for Hurtado's and Nevarez's murders. But unlike Ervin, Zambrana requested an evidentiary hearing on his motion. The district court agreed to Zambrana's request, continued his sentencing hearing, and determined that it would hear evidence regarding Zambrana's motion at the rescheduled sentencing hearing itself.
*628 At the hearing, Zambrana presented nine witnesses in an attempt to show that the government knew of, and suppressed, Arreola's misconduct and his ability to coordinate his testimony with Ripoll and Clinton. For instance, Zambrana called as a witness Trinidad Cruz, an inmate at the MCC who testified that before Zambrana's and Ervin's trial, he, Arreola, and Clinton were transferred together from the MCC to the jail in Porter County, Indiana, and that during the trip Arreola and Clinton "were all talking together." Cruz did not state, however, that Arreola and Clinton were "talking" about their testimony. Zambrana called Ripoll, Arreola, and Clinton to testify as well, but each man denied that they had coordinated their testimony, and further stated that they had not discussed their testimony before trial beyond the discussions to which they had already admitted at trial.
The district court rejected Zambrana's arguments with the same reasoning that it had used to deny Ervin's motion: the evidence of Arreola's misconduct did not warrant a new trial because Arreola had already been thoroughly impeached; there was nothing to suggest that the government knew of or suppressed the evidence of Arreola's misconduct; and even if the government had suppressed the evidence of misconduct, the suppression would not have run afoul of Brady because the evidence was merely cumulative impeachment evidence. The court also determined that though Zambrana showed that Ripoll, Arreola, and Clinton had opportunities to discuss their testimony before trial, he nevertheless failed to point to specific evidence that "the government knew that any conversation between [the three men] took place other than what was disclosed." The court accordingly denied Zambrana's motion for new trial, and subsequently sentenced him to life imprisonment.

II. ANALYSIS
Zambrana and Ervin raise two arguments on appeal. First, Zambrana argues that the district court incorrectly denied his motion to sever the homicide counts in the indictment from the drug-conspiracy counts. Next, Zambrana and Ervin together challenge the district court's denial of their motions for new trial. We address these arguments below.

A. The district court's denial of Zambrana's motion to sever
We first address the district court's denial of Zambrana's motion to sever the homicide counts from the drug-conspiracy counts, a decision that we review for abuse of discretion. See United States v. Rice, 520 F.3d 811, 817 (7th Cir.2008). Under Fed.R.Crim.P. 8(a), an indictment may charge a defendant with two or more offenses in separate counts if the offenses charged "are of the same or similar character, or are based on the same act or transaction, or are connected with or constitute parts of a common scheme or plan." Fed.R.Crim.P. 14(a), however, states that if the joinder of offenses "appears to prejudice a defendant," then the district court may order separate trials for the different offenses. The potential sources of prejudice are many. For instance, the joinder might impermissibly coerce a defendant "into testifying on a count upon which he wishes to remain silent." United States v. Archer, 843 F.2d 1019, 1022 (7th Cir.1988); see also United States v. Nettles, 476 F.3d 508, 516-17 (7th Cir.2007). Likewise, the joinder may prejudice the defendant by creating a "spill-over effect"that is, that the jury relies on evidence presented on one set of counts when reaching a conclusion on the other set. See United States v. Dixon, 184 F.3d 643, 645-46 (7th Cir.1999); United States v. Freland, 141 F.3d 1223, 1226-27 (7th Cir.1998).
*629 But whatever the source of the purported prejudice, the defendant bears a heavy burden on appeal when arguing that the prejudice warranted severance. It is not enough for the defendant to show that separate trials for the charges "`may have provided him with a better opportunity for acquittal.'" Dixon, 184 F.3d at 645 (quoting United States v. Alexander, 135 F.3d 470, 477 (7th Cir.1998)). Instead, the defendant must establish that the denial of severance actually prejudiced him by preventing the jury from arriving at a reliable judgment as to guilt or innocence. See id.; Alexander, 135 F.3d at 477; United States v. Balzano, 916 F.2d 1273, 1282 (7th Cir. 1990).
Here, Zambrana argues that he was "unfairly and materially prejudiced by the joinder of the [h]omicide [c]harges to the [d]rug[conspiracy] [c]harges." Zambrana explains that the joinder "prevented him from testifying in his defense" against the homicide allegations. Specifically, Zambrana continues, but for the joinder of the homicide and drug-conspiracy counts, he would have testified that on the night of Hurtado's and Nevarez's murders he was gambling on riverboats, nowhere near the two men. But because the indictment alleged that he had gambled on riverboats to launder his drug money, Zambrana posits that, had he opted to testify as to his alibi, he would have necessarily implicated himself on the money-laundering counts. Zambrana further contends that the district court was aware that he wished to testify as to his alibi. As he points out, he filed a notice of an affirmative defense, in which he stated that during the period of time that the government had alleged that Hurtado and Nevarez were murdered, he "was gambling on the casino boats." Thus, Zambrana argues, the district court incorrectly concluded that he failed to support his motion to sever by not producing the "specific testimony he intend[ed] to give" regarding the homicide counts.
Zambrana's argument is meritless. When seeking to sever charges on the ground that he wishes to testify to some charges but not to others, a defendant must offer "`a convincing showing that he has both important testimony to give concerning one count and [the] strong need to refrain from testifying on the other.'" Archer, 843 F.2d at 1022 (quoting Baker v. United States, 401 F.2d 958, 977 (D.C.Cir. 1968)); see also Alexander, 135 F.3d at 477. A defendant's "general assertions" about the testimony he seeks to offer will not suffice; he must proffer "specific examples of the exculpatory testimony" that he would give but for the joinder of the counts. Alexander, 135 F.3d at 477; see also Balzano, 916 F.2d at 1283. But in his motion to sever, Zambrana provided no such pointed examples of the "exculpatory testimony" he wished to provide; he merely stated that he "wish[ed] to testify" in his own defense against the homicide counts, but "[t]hat combining all the counts at one trial" would prevent him from doing so. And the fact that Zambrana submitted a notice to present an alibi defense does not mitigate his vague proffered justification for severance. Nowhere in the notice did Zambrana state that he wished to testify that he was gambling when Hurtado and Nevarez were murdered. In fact, Zambrana expressly stated that he would "rely on records provided by the [g]overnment" to establish his alibi, and not on his own testimony. In all, Zambrana presented nothing more than "general assertions" that, absent the severance, he would not be able to testify as to the homicide chargesa showing that was insufficient to show that severance was necessary. See Alexander, 135 F.3d at 477; Balzano, 916 F.2d at 1283.
*630 Zambrana also contends that severance was necessary to avoid a prejudicial "spill-over effect" from the drug-conspiracy counts to the homicide counts. According to Zambrana, the government's case against him on the homicide counts was "weak," and the joinder of the homicide counts with the drug-conspiracy counts caused him to "suffer a spill-over effect of the stronger evidence of the [d]rug[conspiracy] [c]harges onto the more circumstantial and flimsy evidence supporting the [h]omicide [c]harges." Thus, Zambrana argues, "[a]llowing the same jury to hear all of the evidence and decide all of the charges together ... created an unreasonable risk that the jury decided the [h]omicide [c]harges based on the stronger evidence presented in support of the [d]rug [conspiracy] [c]harges."
But Zambrana ignores that the district court instructed the jury to consider each count and its related evidence separately. Specifically, the court instructed the jury to "consider each count and the evidence relating to it separate and apart from every other count." We presume a jury "`attend[s] closely [to] the particular language of the trial court's instructions in a criminal case,'" including when the jury is "`instructed to consider each count and the relating evidence separately.'" United States v. Stokes, 211 F.3d 1039, 1043 (7th Cir.2000) (quoting United States v. Coleman, 22 F.3d 126, 135 (7th Cir.1994), and United States v. Linwood, 142 F.3d 418, 426 (7th Cir.1998)). We find nothing in the record that would make us "`suppose that [the jury] would disregard'" the district court's instructions in this case, and Zambrana points to no evidence that reveals that the jury ignored the court's instructions. Id. (quoting Coleman, 22 F.3d at 135); see also United States v. Stillo, 57 F.3d 553, 557 (7th Cir.1995); United States v. Boykins, 9 F.3d 1278, 1289 (7th Cir.1993). And because the district court's instructions provided "`an adequate safeguard'" against "`evidentiary spillover and cumulation of evidence,'" Balzano, 916 F.2d at 1282 (quoting United States v. Moya-Gomez, 860 F.2d 706, 768 (7th Cir.1988)), we cannot say that Zambrana was prejudiced by the district court's denial of his motion to sever, see United States v. Moore, 363 F.3d 631, 642 (7th Cir.2004) (stating that limiting instruction "adequately handled any risk of prejudice" to defendant), vacated in part by Young v. United States, 543 U.S. 1100, 125 S.Ct. 1019, 160 L.Ed.2d 1001 (2005), and Jackson v. United States, 543 U.S. 1100, 125 S.Ct. 1019, 160 L.Ed.2d 1001 (2005), in light of United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005).

B. The district court's denial of Zambrana's and Ervin's motions for new trial
Next, Zambrana and Ervin both challenge the district court's denial of their motions for new triala decision that also rested within the court's discretion. See United States v. Palivos, 486 F.3d 250, 254 (7th Cir.2007). Zambrana and Ervin each assert that the district court abused that discretion by failing to conduct an evidentiary hearing (in Ervin's case) and by holding an inadequate evidentiary hearing (in Zambrana's case) before denying their motions for new trial. As both men put it, the district court failed to "inform its discretion" when concluding that the evidence of Arreola's misconduct and the government's alleged suppression of that evidence did not justify a new trial, and thus its denial of their motions should be reversed.
However, Zambrana and Ervin have waived any challenge to the manner in which the district court weighed the *631 evidence in support of their motions by failing to object to the court itself regarding the way in which it considered the evidence. See United States v. Haskins, 511 F.3d 688, 693 (7th Cir.2007); United States v. Charles, 476 F.3d 492, 495-96 (7th Cir.2007); United States v. Hernandez-Rivas, 348 F.3d 595, 598 (7th Cir.2003) ("The general rule within the Seventh Circuit is that if a party fails to file an objection with the district court, he or she `waives the right to appeal all issues, both factual and legal.'" (quoting United States v. Brown, 79 F.3d 1499, 1503 (7th Cir. 1996))). Even more, Ervin did not request an evidentiary hearing on his motion, and further accepted the government's representations regarding Arreola's misconduct and the government's lack of knowledge of the misconduct. Similarly, the district court granted Zambrana's request for an evidentiary hearing, and at that hearing he was allowed to present nine witnesses in support of his motion. The district court never attempted to limit the scope of the hearing, and Zambrana never objected to the manner in which the district court held the hearing. And because both men failed to challenge the manner in which the district court considered the evidence related to their motions for new trial, we will not address the issue here. See Haskins, 511 F.3d at 693; Charles, 476 F.3d at 495-96; Hernandez-Rivas, 348 F.3d at 598.
But even if Zambrana and Ervin had preserved their challenges as to how the district court "informed its discretion," the arguments would have failed. Because their substantive arguments in support of their motions for new trial are meritless, any purported procedural deficiency in the manner in which the district court weighed the evidence would have been harmless. See United States v. Kelly, 337 F.3d 897, 901-02 (7th Cir.2003) (holding that district court's failure to hold evidentiary hearing to ascertain whether defendant breached plea agreement was harmless when it was clear defendant breached agreement); see also Pinholster v. Ayers, 525 F.3d 742, 764 (9th Cir.2008) (holding that "any error the district court may have committed" at evidentiary hearing addressing ineffective-assistance-of-counsel claim was harmless because defendant failed to show he was prejudiced by counsel's alleged shortcomings); Wyoming v. Livingston, 443 F.3d 1211, 1225-26 (10th Cir.2006) (stating that district court's failure to hold evidentiary hearing on issue of removal was harmless where evidence clearly supported removal: "In our view, to reverse and remand to the district court for an evidentiary hearing (on nothing), as the State requests, would be a colossal waste of time and resources").
Specifically, the evidence of Arreola's misconduct did not justify a new trial as newly discovered evidence. To obtain a new trial based on newly discovered evidence, a defendant must show, among other things, that the evidence in question "is material and not merely impeaching or cumulative," and that it "probably would lead to an acquittal in the event of a new trial." United States v. Hodges, 315 F.3d 794, 801 (7th Cir.2003). And yet the evidence of Arreola's misconduct is both impeaching and cumulative. The evidence did not show, as Zambrana contended before the district court, that Arreola took advantage of his unmonitored telephone calls and visits in jail to discuss with Ripoll and Clinton how to testify. The most that the evidence shows in that regard is that Arreola could have made an unmonitored telephone call to contact Ripoll or Clinton somehow, and that the three men had opportunities to discuss their testimony while they were detained together, such as when Arreola and Clinton were being transferred from the MCC with Cruz. But there is no evidence that *632 suggests that the three men actually coordinated their testimony. To the contrary, at the evidentiary hearing on Zambrana's motion, Ripoll, Arreola, and Clinton each testified that they did not discuss their trial testimony beyond the discussions that they had already described at trial.
If anything, then, the evidence of Arreola's misconduct would have been relevant to show that he was an untrustworthy, criminal-minded, and manipulative individual who had the propensity for deception and a willingness to break the law. But at trial, Zambrana and Ervin thoroughly impeached Arreola as to his drug-trafficking past, his gang affiliation, his role in Hurtado's and Nevarez's murders, the lies he previously told to the police investigating the murders, and his misconduct at the MCC. Both men even called character witnesses to impugn Arreola's credibility further.
It therefore is unlikely that more evidence describing Arreola's criminal naturethat is, his misconduct at the Hammond City Jailcould sway a new jury to such an extent as to lead it to acquit Zambrana or Ervin. This is particularly so when Arreola was not the only witness to testify that Zambrana and Ervin had helped scheme to rob and to murder Hurtado and Nevarez. See United States v. DePriest, 6 F.3d 1201, 1217 (7th Cir.1993) (relying on United States v. Taglia, 922 F.2d 413, 415 (7th Cir.1991), to determine that newly discovered impeachment evidence did not warrant new trial because conviction was not "premised on the demonstrably dubious testimony of a single witness").
And because the proof of Arreola's misconduct was merely cumulative impeachment evidence, Zambrana's and Ervin's Brady claims necessarily fail. Brady does not extend to "[e]vidence that impeaches an already thoroughly impeached witness." United States v. Kozinski, 16 F.3d 795, 819 (7th Cir.1994); see also United States v. Bailey, 510 F.3d 726, 736 (7th Cir.2007). Although Brady prohibits the government from suppressing evidence that could be used 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); Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972); United States v. Dabney, 498 F.3d 455, 459 (7th Cir. 2007), the evidence must be for "`more than cumulative impeachment,'" Kozinski, 16 F.3d at 819 (quoting United States v. Dweck, 913 F.2d 365, 371 (7th Cir.1990)); see also Bailey, 510 F.3d at 736; United States v. Senn, 129 F.3d 886, 893 (7th Cir.1997) ("Because the defendants did impeach [the witness] on a number of issues, they can't really make a convincing argument that additional impeachment had a reasonable probability of changing the outcome of the trial."). And because Arreola was thoroughly impeached at trial, even if the government had suppressed the evidence of Arreola's misconduct at the Hammond City Jail (which, given the government's explanations, we do not believe to be the case), Zambrana's and Ervin's Brady claims would still fail. See Bailey, 510 F.3d at 736; Kozinski, 16 F.3d at 819. We thus cannot fault the district court for denying Zambrana's and Ervin's motions for new trial.

III. CONCLUSION
We AFFIRM the district court's denial of Zambrana's motion to sever, as well as the district court's denials of Zambrana's and Ervin's motions for new trial.
