
797 A.2d 1251 (2002)
Jerry J. BENNETT, Appellant,
v.
UNITED STATES, Appellee.
Nos. 96-CF-374, 00-CO-682.
District of Columbia Court of Appeals.
Argued January 29, 2002.
Decided May 16, 2002.
*1252 Jenifer Wicks, Washington, DC, for appellant.
Caroline Cahill Shepherd, Assistant United States Attorney, with whom Roscoe C. Howard, Jr., United States Attorney, and John R. Fisher and Thomas J. Tourish, Jr., Assistant United States Attorneys, were on the brief, for appellee.
Before SCHWELB, RUIZ, and WASHINGTON, Associate Judges.
SCHWELB, Associate Judge:
On December 6, 1995, a jury convicted Jerry J. Bennett of first-degree murder while armed, D.C.Code §§ 22-2401 and  3202 (1996),[1] possession of a firearm during a crime of violence (PFCV), D.C.Code § 22-3204(b) (1996),[2] and carrying a pistol without a license (CPWOL), D.C.Code § 22-3204(a) (1996).[3] On March 5, 1999, Bennett filed a post-trial motion to vacate his conviction pursuant to D.C.Code § 23-110, alleging ineffective assistance of counsel at trial. Following an evidentiary *1253 hearing, the trial judge denied Bennett's motion in a four-page written order.
Bennett filed timely appeals from his convictions and from the order denying his post-trial motion. These appeals were consolidated by order of this court. Bennett contends, inter alia, that the trial judge erred by permitting the redaction, from a principal prosecution witness' grand jury testimony which was provided to the defense pursuant to the Jencks Act, 18 U.S.C. § 3500,[4] of material tending to show that she had lied either to the police or to the grand jury with respect to another murder that she had allegedly observed. We agree and reverse.

I.

THE TRIAL COURT PROCEEDINGS

A. Factual background.

These appeals arise out of the murder of Garland Denney in the dark of the night on October 18, 1993. Denney was shot nine times in the head and once in the torso on the front steps of an apartment building in southeast Washington, D.C.
At trial, the government reconstructed the events leading to Denney's murder primarily through the testimony of three women who had purchased drugs from the men involved, and who had used drugs on the evening in question. The women were Delores Smith, Delores' daughter Bnyonka Nabinette, and Delores' niece Donna Smith. All three women considered themselves part of Denney's extended family. None of these witnesses provided any information to the police about the crime until months after the murder. In addition, the prosecution presented no physical evidence identifying the killer; the pistol used to shoot Denney was not recovered.
The prosecution's theory of the case was that Bennett murdered Denney in cold blood in retaliation for Denney's alleged role in an altercation between Bennett and Delores Smith, to whom Denney referred as his aunt. There was testimony that Bennett, Denney, and several other men spent the night of the murder talking and selling drugs in the area where police found Denney's body. Delores Smith, who lived nearby, testified that she had purchased crack cocaine from Denney earlier in the evening. When Ms. Smith approached Denney to make a second purchase, Bennett kicked her, knocking her money from her hand and causing her to fall. Bnyonka Nabinette testified that she subsequently heard Denney say to Bennett, "Don't put [your] feet on [my] aunt no goddamn more."
Ms. Nabinette also testified that, after this altercation, she overheard a conversation between Bennett and someone she called "Little Jay." Little Jay allegedly told Bennett to "leave that shit alone," and he warned Bennett that "you know if you do something to one of them, you're going to have to do something to all of them[.]" According to Ms. Nabinette, Bennett replied: "Fuck them niggers. I'll go down the whole soul train line and I'll kill all them bitch ass niggers." Ms. Nabinette understood Bennett's uncomplimentary characterization as a reference to her extended family.
Delores Smith testified that some time later that evening, while she was standing on the porch of her own building, she looked across to the neighboring porch and saw Bennett point a pistol at Denney.[5] She reported that she ducked inside her building for cover, and that she then heard *1254 a series of gun shots. A short time later, she looked out and saw Denney's dead body on the steps and Bennett "bending the curve" as he ran from the scene. Ms. Nabinette and Donna Smith also reported hearing gun shots. Donna Smith testified that she saw Bennett with a black handgun near the door of the apartment building after she heard the shots. All three witnesses were impeached with prior convictions and drug-related activities.
On December 6, 1995, the jury convicted Bennett of all three counts in the indictment. The judge sentenced Bennett to consecutive prison terms of from thirty years to life for first-degree murder and five to fifteen years for PFCV. Bennett also received a concurrent one-year sentence for CPWOL. Four and one-half years later, on May 5, 2000, Bennett's § 23-110 motion was denied. In these consolidated appeals, Bennett challenges his convictions and the denial of post-trial relief.

B. Redacted information concerning Delores Smith.

The principal issue in this case arises from Delores Smith's grand jury testimony, on the same day, about two unrelated murders that occurred in front of the same house approximately six months apart. The first of these murders was the shooting of Denney, allegedly by appellant Bennett. The second murder was allegedly committed by a man called Spruill.
After Delores Smith had testified on direct examination, the prosecutor provided the defense, in conformity with the Jencks Act, with Ms. Smith's grand jury testimony. The prosecutor, however, redacted substantial portions of Ms. Smith's testimony relating to the Spruill case. Specifically, the prosecutor declined to disclose evidence that Delores Smith had initially given a written statement to the police shortly after the second murder in which she claimed that she was in her apartment at the time of that killing and that she was not a witness to the crime. Before the grand jury, on the other hand, Delores Smith testified that she had witnessed the murder allegedly committed by Spruill from the hallway of the apartment building.
Bennett's attorney, who was aware that the Jencks material had been redacted, requested disclosure of portions of Delores Smith's grand jury testimony which the prosecutor had declined to make available to the defense. The prosecutor provided the requested material to the trial judge in camera at an ex parte bench conference, but he argued that disclosure to the defense of material regarding the crime allegedly committed by Spruill was not necessary. The prosecution conceded that Delores Smith had apparently been untruthful in connection with the second murder, but he argued that this was irrelevant to the prosecution of Bennett.
The trial judge concluded that the redacted portions of Delores Smith's testimony need not be disclosed to Bennett's attorney. The judge further ruled that even if the statements were subject to disclosure, they could not be used to impeach Ms. Smith. The judge first considered the government's duty to disclose evidence adversely affecting the credibility of a government witness under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), but he held that these authorities did not require disclosure. The judge stated:
[A]fter considering the nature of that information that it was not required to be disclosed . . . given the fact that it was her testimony before the grand jury and her prior statement related to an unrelated case. . . . The prior statement was not given under oath. Her grand *1255 jury testimony which . . . appeared to be inconsistent from the prior statement was given under oath.
I believe a significant basis for not requiring you to disclose it was the fact. . . it would not be probative of the issue directly related in this case, given how the testimony was about a different homicide, different people[.]
The judge then ruled that even if the material in question were subject to disclosure, the defense would not be permitted to use it to impeach or cross-examine Delores Smith:
Assuming it is disclosable under Brady, the court ... has determined for the same reasonsthe fact that ... those prior statements or statements made about another case do not bear directly on the witness' veracity in this case or issues in this case; and even if [they do bear on the witness' veracity in this case] the court believes, given the information that's been used in this case to impeach the witness' credibility . . . such as grand jury testimony [that] could establish prior inconsistent statement, the use of drugs to establish the lack of perception, ... the testimony regarding delay in recording the witness' observation, [and] the testimony about the bias that may exist [with] the witness having the case pending in the system. . . .
The court has also concluded that it would only be cumulative of what has already taken place in the case.
Bennett challenges both of these rulings on appeal.

II.

LEGAL ANALYSIS
In essence, the trial judge declined to order disclosure to the defense of the material relating to the second murder because he considered it to be of minor relevance and because he apparently regarded it as cumulative impeachment. Even according the judge's determination a measure of deference,[6] we are unable to agree with his disposition. In our view, the jury in this case was denied information which was of critical importance to its assessment of the evidence.
The question of Bennett's innocence or guilt of a brutal murder turned entirely on the credibility of the witnesses. Delores Smith was perhaps the most important of these witnesses, and the jury was faced with the question whether this witness should be believed when she testified, under oath, regarding Bennett's involvement in a wanton and intentional killing.
Murder is, perhaps, the ultimate crime. To lie to the police or to a grand jury about a murder is to pervert the course of justice with respect to the willful taking of a human life. If a witness is willing to lie about a murder, a jury may well conclude that she is likely to be willing to lie about anything. More particularly, if she has *1256 lied about one murder, there may be little if any reason to credit her testimony about a different murder.
In the present case, the material which the judge permitted the prosecutor to withhold from the defense and the jury apparently showed that Delores Smith had lied, either to the police or to the grand jury, about a murder which she ultimately claimed to have witnessed. She told the police that she had not seen the killing; she told the grand jury that she had. In the absence of some explanation by Ms. Smith of how she gave two irreconcilable accounts relating to the same murder and none was offered to the trial judge by the prosecutordisclosure of the redacted material would have informed the jury in Bennett's case that Delores Smith was a person who was willing to lieeither to the authorities, or to a grand juryabout whether or not she had witnessed the willful murder of another human being. Moreover, the murder about which Delores Smith had lied apparently occurred in essentially the same location as the killing of Denney and only a few months later. In addition, Ms. Smith testified about the two homicides in the same appearance before the grand jury. If the jurors at Bennett's trial had known that Ms. Smith had lied about the killing allegedly perpetrated by Spruill, they would surely have approached her testimony about the murder allegedly committed by Bennett with a substantially increased measure of skepticism. A contrary conclusion cannot be reconciled with human experience or with common sense.
"The refusal by the prosecution to disclose material evidence favorable to the defense deprives the defendant of his liberty without due process of law." Edelen v. United States, 627 A.2d 968, 970 (D.C.1993) (citing Brady, supra, 373 U.S. at 87, 83 S.Ct. 1194). "`[I]mpeaching evidence' is exculpatory and thus can be material to guilt or punishment within the meaning of Brady." Lewis v. United States, 408 A.2d 303, 307 (D.C.1979); see also Strickler v. Green, 527 U.S. 263, 280, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999). There can be no doubt that the redacted evidence, which showed that Delores Smith lied either to the police or to the grand jury about a murder that she allegedly witnessed, was "evidence favorable to the defense." Edelen, supra, 627 A.2d at 970. We must therefore determine whether the withheld evidence was "material," id., i.e., whether "there is a reasonable probability that, had the evidence been disclosed, the result of the proceeding would have been different." Curry v. United States, 658 A.2d 193, 198 (D.C. 1995) (quoting Edelen, supra, 627 A.2d at 971).
In reviewing the trial judge's refusal to require the disclosure of impeachment evidence, we consider the importance of the witness to the government's case, the credibility of the witness, and the value of the withheld evidence in undermining the witness' credibility. See, e.g., Sterling v. United States, 691 A.2d 126, 135 (D.C. 1997). Given the content of her testimony, see page 1253, supra, Delores Smith was an important prosecution witnessshe claimed to have seen the accused point a pistol at the decedent and flee after gunshots were fired, and she also described earlier events that allegedly furnished Bennett with a motive. Although Ms. Smith was significantly impeached on grounds other than her lie about the second murder,[7] none of the other bases for *1257 impeachment can reasonably be considered to be as significant as an apparent outright lie regarding whether or not the witness had or had not personally seen the murder of a human being. In our view, the redacted testimony would potentially have undermined Delores Smith's credibility to a very substantial degree. The government's case, as we have noted, rested entirely on the credibility of its three rather flawed witnesses. We therefore conclude that "there is a reasonable probability that, had the evidence been disclosed, the result of the proceeding would have been different," Edelen, supra, 627 A.2d at 971 (citing Catlett v. United States, 545 A.2d 1202, 1217 (D.C.1988) (citing United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985) (concurring opinion))), and that the trial judge's contrary conclusion cannot be sustained under the Davies standard, 476 A.2d at 661. But cf. note 6, supra.[8]
The trial judge also held that even if the redacted material were subject to disclosure under Brady, the defense would not be entitled to cross-examine or impeach Delores Smith with it. The judge appeared to believe that the evidence was of limited relevance because it concerned a different murder, and also because, since Ms. Smith was otherwise impeached, the cross-examination based on her apparent lies regarding the second murder would have been cumulative. We cannot agree.
The trial judge has broad discretion to "impose reasonable limits" on cross-examination to prevent "interrogation that is repetitive or only marginally relevant." Roundtree v. United States, 581 A.2d 315, 323 (D.C.1990) (quoting Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986)). "[T]he broad discretion afforded the trial court[, however,] cannot justify a curtailment which keeps from the jury relevant and important facts bearing on the trustworthiness of crucial testimony." McCloud v. United States, 781 A.2d 744, 752 (D.C.2001) (quoting Springer v. United States, 388 A.2d 846, 855 (D.C.1978)). In this case, the witness' lie, either to the police or to the grand jury, about whether or not she witnessed the second murder cannot fairly be characterized as "repetitive" or as "only marginally relevant." Roundtree, supra, 581 A.2d at 323. On the contrary, disclosure to the jury that the witness had lied about a different murder would surely have lessened the jurors' trust in her testimony regarding the murder of Denney.
Nor can we agree with the judge's statement that disclosure of the redacted evidence "would only be cumulative of what has already taken place in this case." As we stated in District of Columbia v. Bethel, 567 A.2d 1331, 1336 (D.C.1990),
[a] trial judge has considerable discretion with respect to the admission or exclusion of cumulative evidence. See generally I. & A. Gard, JONES ON EVIDENCE § 1.5 (6th ed. 1972 & Supp.1989), and authorities there cited. Evidence which adds little of probative value to the record may be excluded in order to avoid a waste of time, Mitchell v. Keith, 752 F.2d 385, 392 (9th Cir.), cert. denied, 472 U.S. 1028, 105 S.Ct. 3502, 87 L.Ed.2d 633 (1985), or, as Justice Holmes put it more than a century ago, as "a concession to the shortness of life." *1258 Reeve v. Dennett, 145 Mass. 23, 28, 11 N.E. 938, 943-44 (1887).
But we do not have a case here of "evidence which adds little of probative value to the record." Id. On the contrary, the excluded evidence shows that the witness lied, to the police or to the grand jury, about whether or not she witnessed another murder. Such a lie potentially undermines the witness' credibility in testifying about the murder being tried before the court and is not merely cumulative of other more familiar lines of impeachment. We have held that even where a prosecution witness has been "substantially impeached," the trial court's refusal to permit further and different impeachment may warrant reversal of the defendant's conviction. See, e.g., Brown v. United States, 683 A.2d 118, 127 n. 10 (D.C.1996). Our articulation in Brown applies to this case a fortiori.
If the defense had been permitted to cross-examine Delores Smith about, and impeach her with, her two irreconcilable versions of the second murder, there is, at least, a reasonable probability that her credibility in Bennett's case, already shaky as a result of other impeachment, would have been fatally undermined. "A reasonable jury might have received a significantly different impression of [Delores Smith's] credibility had [Bennett's] counsel been permitted to pursue [her] proposed line of cross-examination." Van Arsdall, supra, 475 U.S. at 680, 106 S.Ct. 1431. Under these circumstances, we cannot sustain the trial judge's refusal to permit such cross-examination and impeachment.[9]

III.

CONCLUSION
For the foregoing reasons, in Number 96-CF-374 Bennett's convictions are reversed. Number 00-CO-682, the appeal from the denial of the post-trial motion, is dismissed as moot. The case is remanded for further proceedings consistent with this opinion.[10]
So ordered.
NOTES
[1]  These provisions have been recodified as D.C.Code §§ 22-2101 (2001) and 22-4502 (2001), respectively.
[2]  This provision has been recodified as D.C.Code § 22-4504(b) (2001).
[3]  This provision has been recodified as D.C.Code § 22-4504(a) (2001).
[4]  See Jencks v. United States, 353 U.S. 657, 77 S.Ct. 1007, 1 L.Ed.2d 1103 (1957).
[5]  Testifying before the grand jury, Delores Smith had stated she did not see Bennett with a handgun and that she could not tell whether he had one.
[6]  See Davies v. United States, 476 A.2d 658, 661 (D.C.1984) (citing United States v. Agurs, 427 U.S. 97, 114, 96 S.Ct. 2392, 49 L.Ed.2d 342 (1976) ("Where, as here, the trial court has determined that asserted Brady material would not have materially affected the verdict, the reviewing court is limited to a determination of whether that decision was reasonable.")). But cf. Farley v. United States, 767 A.2d 225, 228 (D.C.2001) (questioning whether the Davies standard remains in effect); id. at 233 et seq. (Ruiz, J., dissenting) (concluding that an appellate court's review of a Brady ruling is de novo). In its brief in this case, the government states that "[w]hether the trial court erred in not ordering the government to disclose [Delores] Smith's grand jury testimony as Brady material is a question of law and is subject to de novo review by this [c]ourt." Because reversal is required even under the Davies standard, we need not decide whether that standard continues to define our scope of review.
[7]  Delores Smith's grand jury testimony relating to the Denney murder was inconsistent with her trial testimony with respect to whether she saw Bennett with a handgun. Ms. Smith was also impeached with prior convictions for drug distribution and with her long-term drug abuse. In addition, a criminal case against Ms. Smith was pending at the time of trial, and this allegedly provided her with a motive to try to assist the prosecution.
[8]  The government argues that it is not uncommon for a witness initially to deny knowledge of a violent crime but then to testify truthfully when placed under oath. In our view, this goes to the weight to be given to the redacted evidence, not to its admissibility.
[9]  Given our assessment of the importance of the redacted evidence, we conclude that the error in refusing to permit its use for cross-examination and impeachment was not harmless. See, e.g., Scull v. United States, 564 A.2d 1161, 1166 (D.C.1989).
[10]  Our vacation of Bennett's convictions makes it unnecessary for us to reach most of his other claims of error. We hold, however, that the evidence of Bennett's guilt was sufficient to go to the jury, and that the trial judge did not err in denying Bennett's motion for judgment of acquittal. See, e.g., Mills v. United States, 599 A.2d 775, 780-81 (D.C.1991) (articulating standard); In re A.H.B., 491 A.2d 490, 496 n. 8 (D.C.1985) (discussing doctrine of "inherent incredibility"). We also discern no abuse of discretion in the trial court's admission of evidence regarding Bennett's prior possession of a firearm, Martin v. United States, 606 A.2d 120, 132 (D.C.1991), or Bennett's drug distribution. Boone v. United States, 769 A.2d 811, 815-17 (D.C.2001).
