
564 A.2d 1161 (1989)
Alberto Crespo SCULL, Appellant,
v.
UNITED STATES of America, Appellee.
No. 86-1477.
District of Columbia Court of Appeals.
Argued June 9, 1989.
Decided September 29, 1989.
*1162 Bruce Clarke, Public Defender Service, with whom James Klein, Public Defender Service, was on the brief, for appellant.
Steven W. Pelak, Asst. U.S. Atty., for appellee. Jay B. Stephens, U.S. Atty., Michael W. Farrell, Asst. U.S. Atty., at the time the brief was filed, and Sharon M. Collins and G. Paul Howes, Asst. U.S. Attys., were on the brief, for appellee.
Before ROGERS, Chief Judge and MACK and TERRY, Associate Judges.
MACK, Associate Judge:
Appellant Alberto Crespo Scull was allegedly one of two protagonists in a shootout. At his first trial, a jury found him guilty of jumping bail, but was unable to return a verdict on several other counts. At a second trial, a jury found him guilty of two counts of assault with a dangerous weapon and of carrying a pistol without a license, but acquitted him of two counts of assault with intent to kill while armed. On this appeal, Scull urges that by denying his request to cross-examine witnesses as to their motive for testifying, the trial court abridged his Sixth Amendment right to confront witnesses against him. He also maintains that the trial court erroneously admitted "other crimes" evidence that he unlawfully carried a firearm for a month prior to the shootout, and that it erred in permitting two police officers to volunteer testimony effectively contrasting his alleged bad character with the good character of two key government witnesses. Because we find that it was indeed error to deny appellant's request to cross-examine adverse witnesses as to their motive for testifying, we reverse the judgment of the trial court and remand for a new trial.[1]

I
According to the government's evidence, in the early afternoon of March 2, 1983, several young men, including appellant Scull and one Edward Harris, were playing "craps" on the south sidewalk of the 1400 block of Park Road, Northwest. Scull, then thirty-two years old, was described as a six-foot-tall Cuban male with a long, thin face, smooth skin, and short hair. At about 4:30 p.m., after two or three hours of play, Scull and Harris had an altercation. Scull struck Harris, knocking him down. Harris left the scene, but Scull, remaining behind, was overheard angrily describing the encounter to two friends, "Lazador" and "Julio."
Two hours later, Scull and his friend Lazador were seen standing in front of 1448 Park Road, conversing with Julio, who was on the opposite side of the street. At the time, the street was busy with pedestrians. Suddenly, a car stopped a short distance away at the corner of Park Road and Hiatt Place, and Harris and another young man sprang out. When Harris demanded that Scull return some money, a second altercation erupted. Standing in the middle of the road, Scull produced a gun and *1163 fired it at Harris. Pedestrians ran for cover as Harris returned Scull's fire from behind several parked cars. A nine-year-old girl, Jenetta Alredge, was caught in the cross-fire and wounded in her right leg. Scull pursued Harris, and fired after him, as he escaped down Hiatt Place. Scull and Harris had exchanged between five and ten gunshots in the encounter.

II
Three of the seven witnesses who testified at trial[2] knew Scull prior to the gunfight. One of them, Edward Harris, had already confessed that he participated in the shootout, but testified that Scull was uninvolved in it. Two others, Nicola ("Nikki") Wilcox and Okima ("Toni") McCombs, teenagers living in an abandoned building near the scene of the gunfight, made positive identifications of Scull. Nonetheless, defense counsel proffered that Wilcox and McCombs had testified only in hopes of avoiding prosecution on drug distribution charges. A Metropolitan Police detective, David S. Brown, had interviewed Wilcox and McCombs approximately ten times in the fourteen months that elapsed between the shootout and the Scull trial, but at each interview they insisted that they had seen nothing. Then, at an allegedly chance encounter at the District of Columbia Courthouse six days before appellant's then-scheduled trial, they admitted to Detective Brown that they had observed the shootout, and that Scull and Edward Harris were the gunmen.
Of the remaining four witnesses, all of whom were unacquainted with Scull before the shootout, three described a gunman with shoulder-length hair, and one of these observed that he had acne-marked skin. At the time, however, Scull had short hair and smooth skin. Nevertheless, one of the three witnesses was able to pick Scull out of a photo array, at a lineup, and by in-court identification. The fourth witness, unable to identify Scull in a line-up, admitted in court that she was not wearing her eyeglasses when she observed the gunman. Thus the government's identification of Scull depended substantially on the testimony of Wilcox and McCombs.
Scull's counsel moved in limine for permission to cross-examine Wilcox and McCombs about their motive for testifying, hoping to elicit evidence that they were doing so to avoid prosecution for their own illegal conduct. According to Scull's proffer supporting this motion, Edward Harris had assaulted Wilcox and McCombs with a baseball bat on June 22, 1983, three months after the shootout. In investigating this assault, Detective Brown learned from Wilcox and McCombs that they regularly sold marijuana for Harris, and that he had beaten them when they short-changed him on the proceeds from one of their sales. At Scull's trial, Wilcox and McCombs explained that they had repeatedly lied to Detective Brown in telling him that they knew nothing of the shootout for fear of retaliation by Harris, and had only agreed to testify against Scull upon learning that Harris was locked up in connection with his assault on them. Defense counsel sought to undermine this explanation for their change of heart by pointing out they had reported the assault themselves, had been informed of Harris' incarceration as early as September 1983, and were prepared at that time to testify against him. Rather, defense counsel suggested, Wilcox and McCombs testified against Scull to mollify prosecutorial authorities, or perhaps to comply with the terms of a "deal," and thereby escape prosecution.
The trial court denied Scull's motion. It did, however, allow other cross-examination relevant to the issue of bias to proceed unimpeded.[3]


*1164 III
The guaranteed opportunity to cross-examine adverse witnesses is an inherent component of the defendant's Sixth Amendment right of confrontation. Davis v. Alaska, 415 U.S. 308, 315-16, 94 S.Ct. 1105, 1109-10, 39 L.Ed.2d 347 (1974); Jones v. United States, 516 A.2d 513, 517 (D.C. 1986). Nevertheless, that right is subject to reasonable limits imposed at the discretion of the trial judge. Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 1435, 89 L.Ed.2d 674 (1986); Alford v. United States, 282 U.S. 687, 694, 51 S.Ct. 218, 220, 75 L.Ed. 624 (1931); Springer v. United States, 388 A.2d 846, 854 (D.C. 1978). Such limits may be imposed to prevent harassment, prejudice, confusion of the issues, or repetitive, cumulative, or only marginally relevant questioning, Van Arsdall, supra, 475 U.S. at 679, 106 S.Ct. at 1435; Beard v. United States, 535 A.2d 1373, 1379 (D.C.1988); Washington v. United States, 499 A.2d 95, 100-01 (D.C. 1985), to avert danger to or the humiliation of a witness, Springer, supra, 388 A.2d at 854, or "[t]o guard against the danger that counsel will ask `highly prejudicial questions of witnesses with the almost certain knowledge that the insinuations are false.'" Jones, supra, 516 A.2d at 520 (Burgess, J., sitting by designation, dissenting), quoting United States v. Pugh, 141 U.S.App.D.C. 68, 71, 436 F.2d 222, 225 (1970).
Hence, we are loath to allow cross-examination without the establishment of a proper foundation, and
to survive objection, the questioner must proffer "some facts which support a genuine belief" that the witness is biased in the manner asserted. United States v. Fowler, 151 U.S. App.D.C. 79, 81, 465 F.2d 664, 666 (1972); see also Hazel v. United States, 319 A.2d 136, 140 (D.C. 1974) (attorney may not ask questions of witness that are "totally groundless"). In addition, the attorney must proffer facts sufficient to permit the trial judge to evaluate whether the proposed question is probative of bias. See Best v. United States, 328 A.2d 378, 381-82 (D.C.1974); see also Hawkins v. United States, 461 A.2d 1025, 1034 (D.C.1983), cert. denied, 464 U.S. 1052 [104 S.Ct. 734, 79 L.Ed.2d 193] [(1984)]; Flecher v. United States, 358 A.2d [322,] 324 (D.C.), cert. denied, 429 U.S. 977 [97 S.Ct. 486, 50 L.Ed.2d 585] [(1976)].
Jones supra, 516 A.2d at 517. Further, where counsel has information from her own client, which she does not know to be false and which is not "inherently incredible," she has a sufficient good-faith basis for the proposed cross-examination. Hazel, supra, 319 A.2d at 139. In the absence of such a factual foundation, the questioner must articulate a "well reasoned suspicion"[4] rather than "an improbable flight of fancy" to support the proposed cross-examination. Pugh, supra, 141 U.S.App.D.C. at 71, 436 F.2d at 225; see also Jones, supra, 516 A.2d at 520 (Burgess, J., dissenting); Collins v. United States, 491 A.2d 480, 487 (D.C.1985).
In denying appellant's motion to cross-examine Wilcox and McCombs about their possible motivation to testify, the trial court observed that the witnesses' report of their beating by Harris and their testimony that they had sold marijuana did not establish a danger of prosecution. Further, the trial court held, the adducement of evidence concerning the reasons for the beating would be collateral to the issues at bar and would tend to obfuscate the issues at trial; and the admission of the proposed cross-examination would frustrate the trial *1165 court's earlier ruling, at the instance of defense counsel, that reference to the prevalence of drug sales at the scene of the incident be avoided. We examine each of these three grounds for denial in turn.[5]
It is probably true, as the trial court held, that Wilcox's and McCombs' testimony about their beating and about their selling marijuana did not establish a sufficient case against them to make their prosecution possible, since key questions, such as whether they carried and sold usable quantities of marijuana, could still not be answered. This alone, however, was not an affirmative reason to limit cross-examination. While the practical likelihood of prosecution is a valid and necessary part of the Fifth Amendment inquiry concerning self-incrimination, it is irrelevant to the Sixth Amendment issue of witness bias. In evaluating the possibility of bias in adverse testimony, the objective likelihood of prosecution and the subjective intent of the government to prosecute are irrelevant; rather, the witness' subjective belief in the possibility of prosecution is central, since it is this belief that can produce bias. See Washington v. United States, 461 A.2d 1037 (D.C.1983). This is not to say that the likelihood of prosecution must be excluded from the trial court's inquiry. The objective likelihood of prosecution, coupled with an account of the information available to the witness in question, may sometimes be helpful in evaluating the possibility that a witness feared prosecution. Indeed, under certain circumstances, a witness' inattention to the real danger of prosecution may be as plausible as her fear of a prosecution unlikely to proceed. Nevertheless, a mere account of the unlikelihood of prosecution, without some conclusive answer to allegations of a witness' subjective fears, cannot be enough to head off the desired cross-examination.[6]
Further, the trial court erred in dismissing appellant's proposed cross-examination as merely collateral and potentially confusing to the jurors. Bias is always a proper subject of cross-examination, In re C.B.N., 499 A.2d 1215, 1218 (D.C.1985); Springer, supra, 388 A.2d at 855; Hyman v. United States, 342 A.2d 43, 44 (D.C.1975), and the alleged bias or unreliability of a witness is never a collateral issue. In re C.B.N., supra, 499 A.2d at 1218; Johnson v. United States, 418 A.2d 136, 140 (D.C.1980). Accordingly, evidence that tends to show bias, even if extrinsic to issues raised on direct examination, should be admitted. United States v. Abel, 469 U.S. 45, 51, 52, 105 S.Ct. 465, 468, 469, 83 L.Ed.2d 450 (1976); In re C.B.N., supra, 499 A.2d at 1218. Any potentiality of confusion to the jury may be eliminated by proper instructions.[7] To the extent that the proposed cross-examination might show or uncover a bias or motivation underlying Wilcox's and McCombs' testimony, it was relevant and admissible.
The trial court's further holding that admission of the proposed cross-examination would frustrate its earlier ruling, *1166 granted at the instance of defense counsel, excluding references to the prevalence of drug sales at the scene of the shootout, lacked legal foundation. There is no rule compelling trial courts to exclude defense evidence on the basis of wholly distinct evidentiary limitations imposed to protect the defendant. Unquestionably, testimony to the effect that a locality is noted for a high incidence of drug traffic is facially distinct from testimony that a particular witness or witnesses sold drugs. More generally, a ruling granted to protect the defendant from incriminating associations should not be used to prevent him from showing the unreliability of government witnesses, and a ruling for his benefit should not be allowed to have an unforeseen adverse impact on his defense. Accordingly, we must conclude that the trial court erred in denying appellant's motion to cross-examine witnesses about their motivation for testifying.

IV
We are unable to deem this error harmless. In Springer, supra, 388 A.2d at 856, we said that an error of this type reaches constitutional proportions if the trial court has failed to permit "sufficient cross-examination to comport with the requirements of the Sixth Amendment." A "constitutional error" has been defined as "one that is so glaring as to cause a substantial deprivation of the right to a fair trial." Hanson v. State, 684 S.W.2d 337, 339 (Mo.App.1984). These statements are somewhat self-reflexive and therefore rather unenlightening. Where, however, there was a realistic chance that the proposed cross-examination had an impact on the outcome of the trial, there can be little doubt that its exclusion was "a substantial deprivation of the right to a fair trial" and deprived appellant of "sufficient cross-examination to comport with the requirements of the Sixth Amendment." Since the proposed cross-examination might have led the jury to doubt dispositive testimony against appellant, its exclusion was of constitutional dimension. Thus, we must reverse the conviction unless we are able to find the error harmless beyond a reasonable doubt. Delaware v. Van Arsdall, 475 U.S. 673, 681, 684, 106 S.Ct. 1431, 1436, 1438, 89 L.Ed.2d 674 (1986); Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967); Brooks v. United States, 516 A.2d 913, 916 (D.C.1986).
In the case on appeal, the jury was exposed to defense counsel's cross-examination of Wilcox and McCombs about their beating by Harris and their dealings with Detective Brown. It was thus given, as defense counsel suggested, evidence from which it might have inferred bias. Nevertheless, this cross-examination was tied to the rather dubious theory that Wilcox and McCombs were somehow prompted to testify against Scull, despite his innocence, only to insure the conviction of Harris. Cross-examination regarding their own fear of prosecution was entirely excluded in limine. Since the issue of this proposed cross-examination was entirely distinct from that allowed by the trial court, central to the jury's evaluation of the credibility of key witnesses, and admissible, its exclusion was constitutional error.
Moreover, even if the unrelated cross-examination of Wilcox and McCombs were construed to incorporate evidence sufficient to support the liberty-interest theory propounded by appellant, the trial court's ruling could not withstand harmless error analysis. Under our harmless error test, "it must be clear beyond a reasonable doubt `(1) that the defendant would have been convicted without the witness' testimony, or (2) that the restricted line of inquiry would not have weakened the impact of the witness' testimony.'" Springer, supra, 388 A.2d at 856, quoting Note, Constitutional Restraints on the Exclusion of Evidence in the Defendant's Favor: The Implications of Davis v. Alaska, 73 MICH L.REV. 1465, 1473 (1975) (footnote omitted from internal quotation). We stress that, in order to affirm, we must be satisfied that appellant would have been convicted, not that he could have been convicted; this is a test of harmlessness and not of sufficiency. Moreover, appellant was entitled not only to Wilcox's and McCombs' answers to his questions, but to *1167 have the jury exposed to their demeanor in answering them, which might also have undermined its confidence in these witnesses. Barber v. Page, 390 U.S. 719, 725, 88 S.Ct. 1318, 1322, 20 L.Ed.2d 255 (1968).
In this case, appellant apparently succeeded in casting doubt on the reliability of identifications made by the four witnesses who were previously unacquainted with him, and obtained testimony from Harris to the effect that he had not been involved in the shootout. Therefore it cannot be said beyond a reasonable doubt that he would have been convicted without the testimony of the two remaining witnesses against him. Nor can it be said beyond a reasonable doubt that the proposed cross-examination would not have weakened the impact of the remaining witnesses' testimony. Had appellant been allowed to impeach these witnesses as biased by their perceived need to curry favor with the government to protect their own liberty interests, see Lewis v. United States, 408 A.2d 303, 308 (D.C.1979), aff'g Lewis v. United States, 393 A.2d 109 (D.C.1978), it is quite plausible that the jury would have discredited or depreciated their testimony.

V
Because appellant proffered a plausible theory alleging witness bias, and the trial court failed to give a legally compelling reason to limit cross-examination, it was constitutional error to impose such limits. Moreover, this error cannot be deemed harmless beyond a reasonable doubt. Accordingly, the judgment of the trial court is reversed and the case remanded for new trial.
Reversed and remanded.
NOTES
[1]  Accordingly, we find it unnecessary to reach the other two issues on appeal. For retrial purposes, however, and to facilitate a final disposition of the case, we note that "other crimes" evidence includes acts "minimally in the nature of a criminal offense," Bigelow v. United States, 498 A.2d 210, 212 (D.C.1985), and that, where the jury was aware that appellant lacked a gun license, evidence that he publicly possessed and brandished a firearm was "other crimes" evidence. Moreover, in the consideration of "other crimes" evidence or evidence likely to suggest appellant's criminal disposition or arouse the jury against him, it is necessary that the trial court give the jury an immediate instruction warning it, among other things, not to consider that evidence as "tending to show in any other way the defendant's guilt of the offense[s] for which he is on trial." CRIMINAL JURY INSTRUCTIONS FOR THE DISTRICT OF COLUMBIA, No. 2.49 (3d ed. 1978).
[2]  For purposes of the ensuing discussion all references are to Scull's second trial, in which he was found guilty of the matters on appeal.
[3]  The trial court permitted cross-examination of Wilcox and McCombs regarding their dealings with Detective Brown. Further, while expressing reservations about the relevance of the inquiry, the trial court also permitted Wilcox and McCombs to be cross-examined about their beating by Harris, which, defense counsel argued, would support an inference that their desire to see Harris convicted had prompted them to identify Scull as well. The trial court only excluded cross-examination regarding the reason Harris had beaten Wilcox and McCombs, and thus precluded exploration of whether they had testified to avoid prosecution for selling drugs.
[4]  Inasmuch as a proffer is nothing more than an offer to prove factual allegations, and does not consist of their proof itself, the distinction between a proffered "factual foundation" and a "well-reasoned suspicion" may appear tenuous. Thus, the alternative presented in the text may seem little more than an alternate statement of the same approach. It is probably enough to state that the questioner must support any proposal for cross-examination with a credible statement describing the suspected cause of bias in the witness, supported by plausible factual allegations or itself plausible within the framework of facts that neither party has contested.
[5]  The trial judge's three stated reasons for denying appellant's motion boil down to two concerns: first, that the proposed line of questioning would unnecessarily confuse the issue (i.e., it was unnecessary because it did not establish a danger that the witnesses would be prosecuted, and it was confusing because "collateral" to the issues explored on direct examination), and second, that it would frustrate the purposes of the court's earlier order to refrain from referring to the high incidence of drug traffic in the area of the shootout. Significantly, of the three reasons, only two (the "collateral" nature of the proposed cross-examination and the supposed frustration of the court's earlier order) were really affirmative reasons for the limitation. The remaining ground (failure to establish the danger of prosecution) was actually relevant only to the issue of harmless error, since it only answered the issue of the possible impact the cross-examination could have on the credibility of the witnesses. See Springer, supra, 388 A.2d at 856.
[6]  Moreover, an important purpose of cross-examination is exploration, and the trial court must give counsel some leeway to probe for information that she cannot prove before commencing cross-examination. Alford, supra, 282 U.S. at 692, 51 S.Ct. at 219; Best, supra, 328 A.2d at 382 n. 3.
[7]  Of course, unless the contrary appears, we must presume that the jury understands and follows its instructions. Tennessee v. Street, 471 U.S. 409, 415, 105 S.Ct. 2078, 2082, 85 L.Ed.2d 425 (1985); United States v. Felder, 548 A.2d 57, 68 (D.C.1988); Sherrod v. United States, 478 A.2d 644, 659 (D.C.1984).
