
578 F.3d 682 (2009)
UNITED STATES of America, Plaintiff-Appellee,
v.
Anas SALEM, Defendant-Appellant.
No. 08-2034.
United States Court of Appeals, Seventh Circuit.
Argued January 14, 2009.
Decided August 25, 2009.
*683 Michelle L. Jacobs, Gail Joy Hoffman (argued), Jonathan H. Koenig, Office of the United States Attorney, Milwaukee, WI, for Plaintiff-Appellee.
Kathleen M. Quinn (argued), The Bernhoft Law Firm, Milwaukee, WI, for Defendant-Appellant.
Before CUDAHY, KANNE, and TINDER, Circuit Judges.
TINDER, Circuit Judge.
After a hotly contested jury trial, Anas Salem was convicted of witness intimidation, in violation of 18 U.S.C. § 1512(b)(2)(A), and possessing a firearm in furtherance of that offense, in violation of 18 U.S.C. § 924(c)(1)(A)(ii). On appeal, he argues that he deserves a new trial because, until it was too late to be useful, the government failed to turn over evidence that its star witness, Carlos Lopez, was involved in a murder for which he has never been charged. The first hint Salem had of this potential murder charge came moments before Salem was to be sentenced when counsel for the government handed his lawyer a copy of a plea agreement for Benny Martinez, a defendant in another federal criminal case. Martinez admitted in that plea agreement that he had gunned down rival gang member, Adan Sotelo. But the plea agreement also discloses that Martinez wasn't alone during this murder. There with him, lying in wait for Sotelo, was Carlos Lopez.
The plea agreement identifies Lopez by name, and it indicates that Lopez made some form of statement about the murder. Apparently, Lopez described how he and Martinez hid in an alley gangway waiting for Sotelo, and when Sotelo rounded the corner, Martinez shot him to death. Lopez and Martinez then fled the murder scene together, finding refuge at Martinez's grandmother's residence a few blocks away. But Lopez has never been charged with any crime related to his involvement in the Sotelo homicide. That, Salem contends, raises an inference that Lopez curried favor with the government in exchange for his agreeing to testify against Salem. And the fact that evidence of the Sotelo murder was not disclosed to him before trial is why he believes he deserves a new one.
The district court denied his request, though, finding that even if the evidence had been disclosed, there was no reasonable probability of a different verdict. But, on the record before us, we conclude that decision was premature. Lopez's statement about the Sotelo killing has never been turned over to Salem nor has it even been produced to the court. This raises questions about whether other evidence favorable to Salem might be lurking out there and not contained in the record. But Salem didn't get a chance to develop that record, because the court denied his request for an evidentiary hearing. We *684 conclude that was an error. So we remand for such a hearing.

I. Background
Lopez was the alleged victim (and the government's principal witness) on the witness intimidation and gun charges against Salem. At trial, Lopez testified that Salem accused Lopez of being a snitch against the Latin Kings street gang (which he was)[1], and that, along with another Latin King, Marcus Colin, Salem beat him up and threatened to shoot him. Salem's attorney went to some length to attempt to impeach Lopez's credibility. She questioned Lopez about the RICO, drug, and gun charges pending against him, and she raised the inference that Lopez was currying favor with the government. Defense counsel specifically asked Lopez if he had heard of U.S.S.G. § 5K1.1 or knew that cooperating with the government was the only way out from under the mandatory minimums he faced. He denied knowing about any benefit for cooperation but testified that he was cooperating simply because he was a victim.
Several other witnesses, including Lopez's mother, corroborated parts of Lopez's story, though no one testified to seeing the gun or the beating. Photos, however, showed some superficial injuries to Lopez's neck and face, consistent with the beating he says he suffered. The jury convicted Salem, and the district court sentenced him to 144 months of imprisonment.
Shortly after the court entered the judgment, Salem moved for a new trial under Federal Rule of Criminal Procedure 33 based on newly discovered evidence. That evidence, Salem argued, revealed that the government had violated Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). This new evidence came in the form of a plea agreement for another Latin King member named Benny Martinez. The plea agreement, disclosed to Salem's counsel after Salem was convictedin fact, delivered to Salem's counsel just minutes before sentencingrevealed that Martinez had pleaded guilty to the homicide of a rival gang member, Adan Sotelo. The agreement also revealed that Lopez had been involved in Sotelo's murder. Apparently, Lopez had admitted in a statement that Martinez and he hid in an alley waiting for Sotelo, and when Sotelo came around the corner, Martinez gunned him down, and then he and Martinez ran from the murder scene to hide together at the residence of Martinez's grandmother. Lopez had also stated that Sotelo was killed on behalf of his gang, the Latin Kings, to prevent Sotelo, a member of a rival gang (the Spanish Cobras), from retaliating for a Latin Kings shooting that had taken place shortly before the murder.
Salem's counsel requested that the government disclose all materials implicating Lopez in Sotelo's murder. The government turned over several eyewitness and police reports, but none identified the perpetrators by name. Moreover, no report contained any statements by Lopez, even though such statements were referenced in the Martinez plea agreement, and the government has not, at least to this point, disclosed whether such statements actually exist, and if so, in what form or who has them. Lopez, however, has never been charged with any crime related to the Sotelo homicide.
*685 In his Rule 33 motion for new trial, Salem alleged that the evidence of Lopez's involvement in the Sotelo homicide could be used to impeach Lopez's testimony the jury could infer that Lopez was testifying against Salem in exchange for the government not prosecuting Lopez for his participation in the Sotelo homicide. (Even if Lopez was not the triggerman, he still could face accomplice or accessory liability.) Hence, in Salem's view, the government's failure to disclose this evidence before trial violated Brady.
The district court concluded otherwise and, after denying Salem's request for an evidentiary hearing, denied Salem's motion for new trial. The court held that the Sotelo homicide evidence would have been inadmissible, and in any event, would not have given rise to a reasonable probability of a different verdict. Salem appeals that decision.[2]

II. Discussion
Brady requires the government to disclose evidence materially favorable to the accused. Youngblood v. West Virginia, 547 U.S. 867, 869, 126 S.Ct. 2188, 165 L.Ed.2d 269 (2006); Brady, 373 U.S. at 87, 83 S.Ct. 1194. That obligation extends to evidence that tends to impeach a government witness. Youngblood, 547 U.S. at 869, 126 S.Ct. 2188; United States v. Bagley, 473 U.S. 667, 676, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985). Failure to disclose such evidence, whether intentional or inadvertent, can entitle the accused to a new trial. Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). The Brady obligation applies even when the suppressed evidence is known only to police and not to prosecutors. Youngblood, 547 U.S. at 869-70, 126 S.Ct. 2188.
The evidence of the Sotelo homicide was not disclosed prior to trial (the government does not contend that it only learned of this matter after trial) and was arguably favorable to Salem. So Brady's requirement that the undisclosed evidence be materially favorable to the accused is *686 central to this case. The district court found the Sotelo homicide evidence immaterial. That's a decision we review for abuse of discretion. United States v. Palivos, 486 F.3d 250, 255 (7th Cir.2007).
Evidence is material "if there is a `reasonable probability' that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Youngblood, 547 U.S. at 870, 126 S.Ct. 2188 (quoting Strickler, 527 U.S. at 280, 119 S.Ct. 1936); see also Kyles v. Whitley, 514 U.S. 419, 433-34, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995). Of course, this means that only admissible evidence can be material, for only admissible evidence could possibly lead to a different verdict. United States v. Silva, 71 F.3d 667, 670 (7th Cir.1995). To demonstrate a "reasonable probability," Salem must show that the government's nondisclosure "undermine[d] confidence in the verdict." Kyles, 514 U.S. at 435, 115 S.Ct. 1555.
What troubles us about this case is that it appears Salem never had a sufficient opportunity to make that showing. Without an evidentiary hearing, we're left wondering what other evidence about Lopez's involvement in the Sotelo homicide is out there. Cf. United States v. Dimas, 3 F.3d 1015, 1018 (7th Cir.1993) (discussing need for evidentiary hearing where record was inadequate to decide Brady issue). From Martinez's plea agreement, it appears Lopez gave a reasonably detailed statement about the murder, and it implies that the statement was given to law enforcement. And presumably the federal government considers it to be reasonably reliablethe same Office of the United States Attorney that prosecuted Salem included a description of Lopez's statement in the Martinez plea agreement, asserting that it was part of the facts that the government could introduce at a trial of Martinez to prove his guilt of gang-related crimes beyond a reasonable doubt. Yet, neither Salem nor the district court has ever seen that statement. Should there in fact be such a statement, it could seriously undermine Lopez's credibility.
From the government's (and the district court's) perspective, though, that doesn't matter. The evidence would have been inadmissible and, regardless, Lopez was thoroughly impeached at trial and the other witnesses' testimony and the injury photos corroborated his story. So, according to the government, any way you slice it the Sotelo homicide evidence is immaterial.
On the record as it stands now, we cannot be so categorical. Proof of bias or motive to lie is admissible impeachment evidence. United States v. Abel, 469 U.S. 45, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984); see also United States v. Manske, 186 F.3d 770, 777 (7th Cir.1999) ("[Proof of bias] is the quintessentially appropriate topic for cross-examination." (quotation omitted)). Indeed, exposing a witness's motive to lie is a "core value" of the Sixth Amendment's Confrontation Clause. United States v. Recendiz, 557 F.3d 511, 530 (7th Cir.2009) (citing United States v. Smith, 454 F.3d 707, 714 (7th Cir.2006)). And a party may introduce extrinsic evidence to show it. United States v. McGee, 408 F.3d 966, 981-82 (7th Cir.2005). Under these principles, courts routinely admit evidence suggesting a witness curried favor with the government in exchange for his testimony as proof of bias or motive to testify falsely. E.g., United States v. Lindemann, 85 F.3d 1232, 1243 (7th Cir.1996) (citing Abel, 469 U.S. at 53, 105 S.Ct. 465). So though the government is correct that FED.R.EVID. 608(b) would bar Salem's counsel from introducing evidence of the Sotelo homicide to degrade Lopez's character, that evidence could be admissible to demonstrate Lopez's incentive to lie to avoid a murder charge. See Abel, 469 U.S. at 55-56, 105 S.Ct. 465 (discussing how proof of bias *687 differs from evidence prohibited by Rule 608(b)).
The sparse record on the Sotelo homicide seems to have tainted the district court's consideration of admissibility. The court held that the evidence would not have been admissible as proof of bias, because, "There is no evidence that Lopez has received a `pass' for his involvement in the Sotelo murder based on his cooperation in this case, which could bear on his credibility." United States v. Salem, No. 06-CR-181, 2008 WL 3540471, at *6 (E.D.Wis. Aug.13, 2008). The government restates this argument on appeal. The court was correct that the record lacks direct evidence that Lopez was given immunity on a murder charge. But, as it stands now, the record appears to be incomplete. And, from what Martinez's plea agreement says about Lopez's statements to police, it likely is incomplete. If there's some additional evidence contained in law enforcement files that suggests Lopez was involved with the murder, or that he received a benefit for cooperating with the government, such information could prove favorable to Salem. The plea agreement alone suggests that Lopez was a participant in the lying-in-wait murder to protect the Latin Kings' interests, and not a mere witness. And even without a note from the U.S. Attorney or the local D.A. expressly outlining a no-charges-for-testimony quid pro quo, such evidence could be admissible to show Lopez's motive to testify against Salem. However, without an evidentiary hearing, Salem was cut short in demonstrating that Lopez's involvement in the Sotelo homicide shows bias.
The same goes for the government's (and the district court's) comparison to our decision in United States v. Pulido, 69 F.3d 192 (7th Cir.1995), and the argument that the Sotelo homicide evidence would only distract the jury and thus be inadmissible under FED.R.EVID. 403. In Pulido, the defense sought to question one of the government's key witnesses about his potential involvement in a triple murder to suggest that the witness's "uncomfortable status as a murder suspect ... led him to cooperate with the government." 69 F.3d at 199. The district court blocked that line of questioning because the court concluded it would only distract the jury. Id. at 202. We upheld that decision, in part, because the record lacked any evidence that the witness was involved in the murders. Id. Police had "ruled out [the witness] as a suspect in the murders," the witness was not identified as the perpetrator in two police lineups, and a witness to the triple murder stated clearly that the Pulido witness was not at the scene. Id. at 198. In this case, however, the record does not support the notion that Lopez was blameless in the Sotelo murder. In fact, the record implies the opposite. And even though at trial Lopez denied knowing about any benefit whatsoever he might receive for testifying, such as a lower sentence under U.S.S.G. § 5K1.1, he was never asked about the murder and why he hasn't been charged. So notwithstanding any denial of a benefit for testifying, defense counsel was never able to raise the inference of such a benefit for the jury. Without further development of the record, we cannot determine whether the probative value of the Sotelo homicide evidence was substantially outweighed by the danger that such evidence will mislead or confuse the jury. See FED.R.EVID. 403.
The government further contends that this evidence is inadmissible because it's cumulative of other impeachment based on Lopez's motive to lie. This contention dovetails into the second portion of the government's overall argument (accepted by the district court) that the Sotelo homicide is immaterial for Brady purposes. From that perspective, it's just one more *688 shred of impeachment evidence, of which the jury heard a great deal.
We recognize that, ordinarily, newly discovered impeachment evidence will not warrant a new trial under Brady. See, e.g., United States v. Reyes, 542 F.3d 588, 596 (7th Cir.2008). It's often cumulative of other impeachment evidence presented at trial. See, e.g., United States v. Ervin, 540 F.3d 623, 631-32 (7th Cir.2008). But that's not a categorical rule. See United States v. Taglia, 922 F.2d 413, 415 (7th Cir.1991). We've recognized that in some instances, such as when the government's case rests "entirely on the uncorroborated testimony of a single witness," new impeachment evidence could be material. Id.
True, Lopez was not the government's only witness and his testimony was corroborated to some extent. But he was the government's star witnesswithout him, there simply is no case at all on these charges. No other witness saw a gun or the beating. Nor was the other evidence in any way overwhelming. For example, Lopez's friend, Shane Bach, testified that he was with Lopez early on the night of the crime in question. Bach testified that he heard Salem ask Lopez why he was "snitching" and heard Salem or Marcus Colin ask the other whether he had "one in the chamber," referring to whether a gun was loaded and ready to fire. But Bach never saw the gun. And Bach later admitted that he never heard Salem threaten Lopez and that they were talking about people who they heard were cooperating against the Latin Kings. Bach also did not witness the alleged beating.
Lopez's mother also corroborated part of her son's storyshe said she saw Lopez with Salem earlier in the evening and Lopez looked worried while he scrambled around the house looking for "paperwork" (which Lopez testified he told Salem was how he would prove that he wasn't a snitch). Lopez's mother saw Lopez leave, and testified that when we came back, he had injuries to his neck and face (which the photos also confirmed). But again, Lopez's mother never saw a gun, nor heard any threats or intimidation. And a mother's desire not to see her son behind bars might also decrease the weight of her testimony, though we recognize that to be a jury concern, not ours.
The only other relevant witness was an FBI Agent who interviewed Marcus Colin, who refused to testify after being called to the stand. But the way in which information from Colin's interview came into evidence was odd. Though being called to the stand by the defense, the agent mentioned that Colin told him that Salem had a gun and had orchestrated the Lopez kidnapping. Beyond its strange introduction, we see other reasons to question the impact of this testimony. The government didn't mention it at closing arguments nor in its appellate briefs. And the district court didn't mention it in its opinion either. So it's debatable whether this testimony reached the jury's ears with any force.
In the end, this case came down to whether the jury believed Lopez's story. He was the victim. No other witness provided a complete narrative, start to finish, of the events that led to Salem's charges. No one saw the gun, heard the threats, or saw the beating. Other evidence corroborated only bits and pieces of Lopez's account. So his credibility was crucial, and bottom line, was the only real issue the jury had to decide.
Nonetheless, as the government points out, Salem's counsel attempted to attack Lopez's credibility at trial by asking him about his motive to lie. Counsel crossexamined Lopez on the RICO, drug, and gun counts that he was facing, some of which carried a maximum sentence of life in prison and mandatory minimums of five *689 and ten years. And she asked whether Lopez was testifying in exchange for leniency-she specifically asked whether he had heard of "substantial assistance" and U.S.S.G. § 5K1.1. Though Lopez denied it, Salem's counsel tried to raise the inference of an incentive to testify falsely to curry favor with the government. This is essentially the same basis on which Salem would seek to introduce the Sotelo homicide matter.
Still, on the sparse record before us, we are unconvinced that every possible piece of evidence of Lopez's participation in the Sotelo homicide must be immaterial. This is not just evidence of another drug or gun crime. Murder is fundamentally different from other offenses. As the Supreme Court recently acknowledged, "there is a distinction between intentional first-degree murder on the one hand and nonhomicide crimes against individual persons, even including child rape, on the other." Kennedy v. Louisiana, ___ U.S. ___, 128 S.Ct. 2641, 2660, 171 L.Ed.2d 525 (2008). All other crimes against individuals "cannot be compared to murder in their `severity and irrevocability.'" Id. (citing Coker v. Georgia, 433 U.S. 584, 598, 97 S.Ct. 2861, 53 L.Ed.2d 982 (1977)). Indeed, first-degree murder holds a unique position in our society's notion of criminality. That first-degree murder is the only crime against the person that commands the death penalty, the Justices have observed, "is an expression of the community's belief that certain crimes are themselves so grievous an affront to humanity that the only adequate response may be the penalty of death." Gregg v. Georgia, 428 U.S. 153, 184, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). So to say that there is no reasonable probability that the jury could reach a different result, even if the evidence showed that the government's star witness was never charged for his direct involvement in a violent gang murder, ignores the differences between the drug and gun crimes about which Lopez was questioned and first-degree homicide.
Not only does society view murder differently than other crimes, but so might Lopez, which could show an enhanced incentive to lie. For impeachment purposes, a criminal defendant on trial is entitled to reveal to the jury not only what benefits a witness is receiving, but also what he perceives he may receive. As we just noted, murder puts a different kind of penalty in play. Though murder is not generally a federal offense, and Wisconsin does not have the death penalty (Wisconsin's stiffest sentence is life without parole, see WIS. STAT. §§ 940.01(1); 939.50(3)(a); 973.014(1g)), Lopez faced charges under RICO for his gang-related activities. Murder committed "for the purpose of ... maintaining or increasing position in an enterprise engaged in racketeering activity" is punishable by death. 18 U.S.C. § 1959(a)(1). So although Salem's counsel made the jury aware of Lopez's possible life sentences, the jury never heard about a possible sentence of death. (And it did not hear about the potential effect of a Wisconsin murder sentence of life without parole.) If agreeing to testify meant the difference between life and death, the jury might have inferred that Lopez had an even more powerful incentive to take the stand and testify favorably for the government. In this sense, though impeaching, evidence of the Sotelo murder might not be cumulative of other impeachment evidence.[3] On this record, though, we cannot *690 come to a firm conclusion on this important question.
To be sure, we are not granting Salem a new trial. But we are not affirming the denial of one either. Without a fuller record, we cannot sufficiently review whether the Sotelo homicide evidence was material. The record indicates that at least some evidence, that of a statement of Lopez himself and the conditions under which he made it, is still unrevealed. With that in mind, we recall our opinion in United States v. Dimas, which reflects precisely the rationale for our decision in this case:
Though we recognize the experienced district judge's familiarity with all aspects of this case, the somewhat sparse record leaves us with serious questions about what impact the Brady material might have had on the jury. Because of these lingering doubts we feel compelled to vacate the order denying a new trial and remand for the limited purpose of allowing the district court to hold an evidentiary hearing on this issue.
Dimas, 3 F.3d at 1018 (citing Barkauskas v. Lane, 878 F.2d 1031, 1034 (7th Cir. 1989)). On remand, the court must first satisfy itself that all the evidence of Lopez's role in the Sotelo homicide has been turned over. Then the court should consider whether the evidence was actually suppressed by the prosecution and whether Salem could have uncovered it with reasonable diligence. Id. at 1018-19. Next, the court should reexamine the admissibility of that evidence. Id. at 1019. Finally, should the court conclude the evidence would be admissible, the court should examine whether there is a reasonable probability that the outcome in Salem's case would change. Id.

III. Conclusion
We VACATE the denial of Salem's motion for a new trial and REMAND for an evidentiary hearing consistent with this opinion.
NOTES
[1]  In the fall of 2005, that investigation resulted in an indictment charging 49 gang members, including Lopez, Salem's brother, Sadam, and fellow Latin King, Marcus Colin, with racketeering and related crimes. In addition to the RICO count, Lopez was hit with a number of drug and gun counts, some of which carried mandatory minimums, consecutive sentences, and statutory maximums of life in prison.
[2]  A brief jurisdictional note before we address Salem's claim on the merits. Ordinarily, when a district court denies a Rule 33 motion for new trial based on newly discovered evidence, we require the party to file a separate notice of appeal after the district court rules on the Rule 33 motion, even if the defendant has already appealed his conviction. See United States v. Harvey, 959 F.2d 1371, 1377 (7th Cir. 1992) ("When a district court denies a motion for new trial while an appeal from the underlying judgment is pending, a separate, timely notice of appeal `is a jurisdictional predicate to appellate review' of the denial of the new trial motion."); see also Johnson v. United States, 246 F.3d 655, 658-59 (6th Cir. 2001); United States v. Douglas, 874 F.2d 1145, 1162 (7th Cir. 1989); cf. Ammons v. Gerlinger, 547 F.3d 724, 726 (7th Cir.2008) (per curiam) (discussing failure to file second notice of appeal and lack of jurisdiction in civil cases); Kitchen v. United States, 227 F.3d 1014, 1017-22 (7th Cir.2000) (same, in ineffective-assistance-of-counsel context). But see United States v. Thornton, 1 F.3d 149, 157-58 (3d Cir. 1993) (holding that appellate jurisdiction of denial of motion for new trial not contingent on second notice of appeal); United States v. Davis, 960 F.2d 820, 824 (9th Cir. 1992) (same); United States v. Wilson, 894 F.2d 1245, 1251-52 (11th Cir.1990) (same); United States v. Burns, 668 F.2d 855, 858 (5th Cir. 1982) (same).

Salem filed only one notice of appeal and did so months before the district court denied his motion for new trial. So ordinarily Salem would need a second notice. However, if a defendant files his motion for new trial based on newly discovered evidence no later than 10 days after entry of the judgment, a second notice is not required. See Fed. R.App. P. 4(b)(3)(C) and 4(b)(3)(A)(ii); Trenkler v. United States, 268 F.3d 16, 21 & n. 4 (1st Cir.2001); cf. Ammons, 547 F.3d at 726 (explaining 10-day rule in civil cases). Salem filed his Rule 33 motion only 7 days after the judgment was entered. Being within the 10-day limit, Salem's first notice of appeal gives us jurisdiction to hear his appeal of the district court's denial of his Rule 33 motion.
[3]  Moreover, Lopez across the board denied any knowledge of any benefit for testifying. Of course, the jury was free not to believe him. But his not admitting to even being aware of "substantial assistance" or U.S.S.G. § 5K1.1 diminishes the value of the impeachment evidence by some measure, however slight.
