
568 A.2d 1079 (1990)
Charles L. VAN NESS, a/k/a Charles Jackson, Appellant,
v.
UNITED STATES, Appellee.
No. 88-145.
District of Columbia Court of Appeals.
Argued October 26, 1989.
Decided January 17, 1990.
Rosemary Herbert, with whom James Klein, Public Defender Service, was on the brief, for appellant.
*1080 Per A. Ramfjord, Asst. U.S. Atty., with whom Jay B. Stephens, U.S. Atty., Michael W. Farrell, Asst. U.S. Atty. at the time the brief was filed, and Ellen Bass, Asst. U.S. Atty., were on the brief, for appellee.
Before NEWMAN and SCHWELB, Associate Judges, and GALLAGHER, Senior Judge.
GALLAGHER, Senior Judge:
After a jury trial, appellant was convicted for distribution of cocaine in violation of D.C.Code § 33-541(a)(1) (1989 Repl.). He contends that the trial court committed reversible error in (1) denying defense counsel the opportunity to cross-examine a government witness regarding his bias, and (2) refusing to order a mistrial or give a requested instruction to mitigate the impact of prosecutorial misconduct. We affirm.

I.
Appellant first contends that the trial court's restriction of cross-examination resulted in reversible error. He argues that all inquiry was foreclosed "on the crucial subject of bias."[1]
The segment of the cross-examination at issue, is as follows:
Q. Good afternoon, officer.
A. Good afternoon.
Q. Now you  You told us on direct examination, and again on cross-examination, that you had been a police officer for about two years  or I should say about a year and a half at the time of March of 1987?
A. That's correct.
Q. And when you became a police officer did you want to become an undercover officer?
MS. BASS: Objection.
THE COURT: Sustained.
MR. BROWN: Your Honor, may we approach the bench?
THE COURT: No, sir, the objection is sustained.
BY MR. BROWN:
Q. Officer Thompson, are you still working as an undercover officer?
MS. BASS: Objection.
THE COURT: Sustained.
BY MR. BROWN:
Q. Officer, your performance is evaluated by your superiors 
MS. BASS: Objection.
THE COURT: Sustained.
MR. BROWN: Your Honor, may we approach the bench?
THE COURT: Yes, sir.
(Thereupon, the witness stepped down from the witness stand, counsel for both parties approached the bench and conferred with the Court, as follows:)
THE COURT: Yes Mr. Brown?
MR. BROWN: Your Honor, the area that I'm attempting to get into is this Officer's bias as an undercover officer to try to make as many arrests as he can. And what I'm trying to get into is that his performance as an officer, evaluation of his performance as an officer is based in, in part, on the number of arrests that result from his undercover buys. My good faith basis for that is testimony from a 5th District vice officer  undercover officer in another case who admitted, during testimony, that one of the bases for evaluation is whether arrests are made on the basis of their undercover operations.
MS. BASS: Your Honor, I'm going to withdraw my objection to the question of whether their evaluations are based on the number of arrests made.
MR. BROWN: As a factor.
THE COURT: Counsel, I want to be careful in avoiding this becoming a free for all. What about the Government's ability to go back into this area on redirect, Mr. Brown?
MR. BROWN: I expect Ms. Bass to ask the Officer at least whether or not his evaluation is based solely on the number of arrests he makes, his answer will be *1081 no. But I want to elicit that it is certainly a factor  elicit  as well as  as long as we are up here  that this is part of Operation Clean Sweep.
MS. BASS: Well, I object to that.
MR. BROWN: And one of the things the police try to do in terms of Operation Clean Sweep is make plenty of drug arrests.
THE COURT: Part of my function as a trial judge is to avoid problems that I'm going to have to resolve later on these evidentiary issues. And I think, even in the absence of a Government objection, you are not going to be allowed to go into that, Mr. Brown, because I can see too many problems I'm going to have to resolve later, whether the objection is made by the Government, or by the Court, sua sponte.
MR. BROWN: Your Honor, what about the Operation Clean Sweep issue?
THE COURT: What about it?
MR. BROWN: What I would like to ask the Officer is whether this was part of Operation Clean Sweep. My good faith basis is that it written on the report  (sic)
THE COURT: What comes after that?
MR. BROWN: The question after that, what is Operation Clean Sweep, the Officer will define it. I will ask him whether or not one of the purposes of Operation Clean Sweep is to make a lot of drug arrests.
MS. BASS: I object to that as being irrelevant.
MR. BROWN: Your Honor, it goes directly to the bias of this Officer to think that this Officer's motive to try to make cases against as many people as he possibly can, to make weak cases into stronger cases.
THE COURT: Where do you go after that? Isn't the purpose of Operation Clean Sweep to make a lot of drug arrests?
MR. BROWN: Yes.
THE COURT: Where do you go after that?
MR. BROWN: After that, Your Honor, I go to 
THE COURT: Any further inquiry into this area? I know what you are leading up to, again and you won't get there. I will allow that question, but you are not going to get through the back door, the side door, or any other door, to that same issue that I'm sustaining an objection, about evaluations being based on arrests. So you can approach it from as many different angles as you want, you still will not get there.
MS. BASS: For the record I do object to the Clean Sweep line of questions, I think it is irrelevant.
THE COURT: Okay.
MR. BROWN: Is the Court going to permit me to ask about Operation Clean Sweep?
THE COURT: I just indicated that I will allow you the preliminary questions, but we both know what you are leading to, and you already know what my ruling is going to be once you get to that point. You have made your record, haven't you, Mr. Brown, or do you wish to add more?
MR. BROWN: I think I have said what I needed to say.
THE COURT: Thank you.
(Thereupon, the proceedings had at the bench were concluded, counsel returned to their seats at counsel table, and the witness returned to the witness stand and testified further, as follows):
THE COURT: Objection to the last question is sustained. Your next question, Mr. Brown.
BY MR. BROWN;
Q. Officer Thompson, in March of 1987, specifically on March 21st, 1987, your involvement in the incident that led to this case was part of what is called Operation Clean Sweep, wasn't it?

A. Correct.
Q. What is Operation Clean Sweep?
A. Operation Clean Sweep is  Well, the name that they gave it to stop the drug sales in the Washington, D.C. area.

Q. And as part of Operation Clean Sweep your mission on March 21st, *1082 1987, was to make drug arrests, is that correct?

A. That's correct.
Q. And part of your mission, as part of Operation Clean Sweep, was to make as many drug arrests as you could, isn't that correct?
A. I don't know.
Q. You don't know?
A. No.
Q. Were you briefed on Operation Clean Sweep before you went out?
MS. BASS: Objection.
THE COURT: Sustained.
BY MR. BROWN:
Q. Were  Do you know, Officer, whether statistics were being kept about the results of Operation Clean Sweep?
A. No, I do not.
MS. BASS: Objection.
THE COURT: Sustained.
BY MR. BROWN:
Q. Officer Thompson, in your capacity as an undercover officer when you're trying to make illegal drug buys, one of your purposes is to deceive the individuals you are speaking with, isn't that correct?

A. No, not necessarily.
Q. Well, you don't tell them you are a police officer, do you?
A. No, I do not.
Q. And you don't tell them, of course, that you are giving them marked money, is that correct?
A. That's correct.
Q. So you try to deceive them, don't you?
A. If you put it like that, yes.
Q. And it is in fact your job as an undercover officer to deceive people, isn't it?
MS. BASS: Objection.
THE COURT: Sustained.

(Emphasis added.)
It is apparent from the foregoing excerpts that the cross-examiner asked and received answers to his questions concerning Operation Clean Sweep, e.g., that the mission of Operation Clean Sweep was "to stop the drug sales in the Washington, D.C. area"; and that part of the officer's "mission" was to make drug arrests. In answer to the question whether part of his mission "was to make as many drug arrests as you could," the officer replied, "I don't know." When asked if he knew "whether statistics were being kept about the results of Operation Clean Sweep, he replied he did not know. Further exploration along this line was terminated by the court.
The cross-examiner then by several questions explored with the officer whether in his "capacity as an undercover officer when you're trying to make illegal drug buys, one of your purposes is to deceive the individuals you are speaking with, isn't that correct?" The officer replied "[n]o, not necessarily." But, he then agreed that he did not tell them he is a police officer; and did not tell them he is giving them marked money. At this point, the cross-examiner asked "[s]o you try to deceive them, don't you?" The officer agreed.
The court then terminated the meaningless cross-examination on this particular point, as it should have.
As is seen, appellant availed himself of an opportunity to cross-examine to some degree on his "bias issue." While the trial court might have permitted a limited further examination on the subject, we surely do not perceive prejudicial error. As a matter of fact, the cross-examination on the ethical aspect of undercover investigation, which was a portion of the restricted cross-examination, did not deserve to be taken seriously.
The cross-examination of the officer, including colloquies, consumed eighty-five pages of transcript, which is a considerable cross-examination of an officer on a street-sale-of-drugs charge.
On this record, we conclude the restriction of cross-examination did not result in reversible error. Singletary v. United States, 383 A.2d 1064, 1073 (D.C.1978).

II.
Appellant next contends that the trial court erred by failing to grant a mistrial or *1083 give curative instructions to mitigate the impact of prosecutorial misconduct. According to appellant, the prosecutor improperly argued that because appellant identified himself as Charles Jackson when arrested and his legal name is Charles Van Ness, appellant was conscious of his guilt at the time.
Although there was uncontroverted evidence that appellant did not use his legal name when arrested, he contends that there was no evidence that the name he gave was an "alias," or a "false name," as the prosecutor characterized it. Appellant argues that the use of a name other than one's legal name may not evidence criminal activity; a person may be commonly known by another name, or may have experienced a change in family circumstances which will prompt him to adopt a new name. Thus, appellant contends that the prosecutor could not argue that appellant's use of a different name, without more, evidenced a consciousness of guilt.
This court has held that a defendant's use of a name different from his own can support an inference that he was conscious of his guilt. Reavis v. United States, 395 A.2d 75, 77 n. 2 (D.C.1978). Thus, the prosecutor's reference to appellant's use of an "alias" did not constitute prosecutorial misconduct.
Appellant also contends that the trial court abused its discretion when it refused to instruct the jury that use of another name may be consistent with innocent behavior. The judge based his refusal on the fact that the prosecutor's argument regarding the "alias" was supported by the evidence, and on his concern that because the prosecutor's references to the "alias" were brief, a curative instruction would only accentuate any improper inferences. This determination by the trial judge was consistent with that of other courts, which have sometimes discouraged the use of instructions regarding post-crime behavior on the ground that such instructions only accentuate the behavior. See United States v. Telfaire, 152 U.S.App.D.C. 146, 152, 469 F.2d 552, 558 (1972). Thus, the trial court did not err when it refused to grant appellant's request for a curative instruction based on the prosecutor's remarks.
Affirmed.
SCHWELB, Associate Judge, concurring in part and dissenting in part:

I
By one satirical account, police officers in Victorian England were said to harbor especially tender and libertarian sentiments towards those whom they were obliged by duty to take into custody. In the words of an immortal Savoyard Sergeant of Police,
[i]t is most distressing to us to be the agents whereby our erring fellow-creatures are deprived of that liberty which is so dear to all  but we should have thought of that before we joined the Force.
WILLIAM S. GILBERT & ARTHUR SULLIVAN, THE PIRATES OF PENZANCE, ACT II (1879). It was, in part, this generous spirit that brought the Sergeant to the melancholy realization that
When constabulary duty's to be done
A policeman's lot is not a happy one.
Id.
Perspective, however, can make a big difference to one's perceptions. Unlike amused librettists, criminal defendants who face mandatory minimum sentences or other constraints on their freedom are not always convinced that officers are especially reluctant to adorn them with handcuffs. Indeed, their attorneys sometimes claim to discern in the criteria for promotions which are actually or supposedly used by police authorities an incentive for officers to arrest as many people as possible, and thus to be a bit careless about making sure that the guy they have brought in is really the one who did it. Understandably, defense counsel would like to plant this notion in the minds of the jurors in the hope that the acorn will grow into an oak and will help to support an edifice of reasonable doubt which will free their beleagured client.
*1084 The present case raises the question whether the defense may cross-examine a police officer with respect to whether his performance evaluation would be based in part on the number of arrests that result from his undercover buys. Van Ness contends that by foreclosing such inquiry by his counsel, the judge improperly restricted the scope of his cross-examination into the officer's possible bias. Although this question comes up with some frequency in the trial court, this court has never decided it. It is squarely presented here, and in my opinion we ought to address it. On the merits, I would hold that the inquiry ought to have been allowed.

II
The basic legal principles are not in dispute. The opportunity to confront and cross-examine prosecution witnesses is guaranteed by the Sixth Amendment and is an essential part of the right to conduct an effective defense. Davis v. Alaska, 415 U.S. 308, 315-316, 94 S.Ct. 1105, 1109-1110, 39 L.Ed.2d 347 (1974). In our adversary system, cross-examination plays a crucial role in uncovering the truth. It ensures the integrity of the fact-finding process. Indeed, "[c]ross-examination is the principal means by which the believability of a witness and the truth of his testimony are tested." Id. at 316, 94 S.Ct. at 1110; see also Kentucky v. Stincer, 482 U.S. 730, 736, 107 S.Ct. 2658, 2662, 96 L.Ed.2d 631 (1987).
Exploration of the bias of a witness may demonstrate that he has a motive to lie, and can therefore be crucial to the jury's assessment of his credibility. Scull v. United States, 564 A.2d 1161, 1165 (D.C. 1989); In re C.B.N., 499 A.2d 1215, 1218 (D.C.1985). A showing of bias or partiality can make the difference between conviction and acquittal. Pennsylvania v. Ritchie, 480 U.S. 39, 51-52, 107 S.Ct. 989, 998-99, 94 L.Ed.2d 40 (1987) (plurality opinion). Accordingly, inquiry into the possible bias of a prosecution witness may not be foreclosed or unreasonably restricted. To the contrary, "the partiality of a witness is subject to exploration at trial, and is `always relevant as discrediting the witness and affecting the weight of his testimony.'" Davis, supra, 415 U.S. at 316, 94 S.Ct. at 1110 (quoting 3A J. WIGMORE, EVIDENCE § 940, at 775 (Chadbourn rev. ed. 1970)); see also Alford v. United States, 282 U.S. 687, 691-94, 51 S.Ct. 218, 219-20, 75 L.Ed. 624 (1931).
Among the conditions or circumstances that may induce bias is, of course, the witness' self-interest. United States v. Abel, 469 U.S. 45, 52, 105 S.Ct. 465, 469, 83 L.Ed.2d 450 (1984). The courts "have recognized that the exposure of a witness' motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination." Davis, supra, 415 U.S. at 316-17, 94 S.Ct. at 1110.
Although the opportunity to cross-examine witnesses regarding potential bias is inherent in the Sixth Amendment right to confrontation, however, the extent of such cross-examination is left to the sound discretion of the trial court. Springer v. United States, 388 A.2d 846, 854 (D.C. 1978); see Alford, supra, 282 U.S. at 694, 51 S.Ct. at 220. As the Supreme Court observed in Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 294, 88 L.Ed.2d 15 (1985) (per curiam), "the Confrontation Clause guarantees an opportunity for effective cross-examination, not cross-examination that is effective in whatever way, and to whatever extent, the defense might wish." See also Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 1435, 89 L.Ed.2d 674 (1986). So long as some "meaningful degree of cross-examination [has been] allowed in the first instance," Springer, supra, 388 A.2d at 845, or the "jury [is] aware of sufficient facts, and [has] heard sufficient testimony, from which it could infer" bias, Beynum v. United States, 480 A.2d 698, 707 (D.C. 1984), the requirements of the Sixth Amendment are deemed to have been satisfied. Accordingly, it is within the discretion of the trial court to limit cross-examination to prevent inquiry into matters having little relevance or probative value. Van Arsdall, supra, 475 U.S. at 679, 106 S.Ct. at 1435; Springer, supra, 388 A.2d at *1085 854-55. If sufficient evidence has been admitted to place the witness' potential bias before the jury, the court may restrict "further cross-examination designed to probe the same potential bias" on the grounds that the probative value of such additional questioning would be outweighed by its prejudice to the government. Reed v. United States, 452 A.2d 1173, 1178 (D.C.1982), cert. denied, 464 U.S. 839, 104 S.Ct. 132, 78 L.Ed.2d 127 (1983).

III
Several courts in other jurisdictions have applied the foregoing principles to issues similar to the one which Van Ness raises here. They have utilized different approaches and have reached different results. I consider those decisions in chronological order.
In State v. Baril, 127 Vt. 394, 250 A.2d 732 (1969), the defendant was convicted of speeding. At trial, he had sought to interrogate the arresting officer on the number of arrests which the officer had made during a three-month period. He offered to show that the number of arrests was one of the factors considered in an officer's promotion. The trial judge sustained the prosecutor's objection to the question. The Supreme Court of Vermont held that the judge's decision was a proper exercise of his discretion. The court said:
The subject, which the respondent tried to present to the jury, was entirely foreign to the issue of the speed of the respondent's vehicle at the time and place alleged. It was remote and speculative in its bearing on the officer's interest in the outcome of the trial. The question was properly excluded.
Id. at 400, 250 A.2d at 736.
In United States v. Williamson, 424 F.2d 353 (5th Cir.1970), a defendant charged with a "moonshine whiskey" offense presented a defense of entrapment. In furtherance of that defense, he sought to cross-examine an Alcohol Tax Unit (ATU) agent as to a number of matters which were alleged to be relevant to the agent's credibility. One of the subjects into which Williamson wished to inquire was the role of arrests in determining the efficiency ratings of ATU agents. The trial judge sustained the prosecutor's objection, and Williamson was found guilty. While reversing the conviction on other grounds, the appellate court stated, without elaboration, that "it was not error for the trial court to sustain objections to these questions." Id. at 356.
In Haeger v. State, 181 Ind.App. 5, 390 N.E.2d 239 (1979), the defendant was charged with driving under the influence of intoxicating liquors. He attempted to question the arresting officer on cross-examination as to whether or not the officer was subject to any quota or requirement that he make a minimum number of arrests within a given period of time. The trial judge sustained an objection to this line of inquiry. The appellate court reversed the conviction, relying in part on this court's decision in Springer. The court said:
Haeger's conviction is based on the testimony of the arresting officer and the results of a Breathalyzer test administered by the same officer. The accuracy of a Breathalyzer test depends on several outside factors, including of course proper operation. Thus, all the evidence in some degree depends on the credibility of this officer. The trial court prevented any mention of whether the officer felt pressure to make a certain number of arrests from reaching the jury. This would be reversible error per se according to Springer.[1]
Id. at 9, 390 N.E.2d at 242. The court noted the contrary holding of the Supreme Court of Vermont in Baril, supra, but stated that Baril was "decided prior to Davis v. Alaska, supra and is apparently *1086 no longer followed." Id. at 7, 390 N.E.2d at 241.
In State v. Bartkowski, 290 N.W.2d 218 (N.D.1980), the defendant asserted an entrapment defense to a charge of possessing a hallucinogenic drug with intent to distribute it. He attempted to cross-examine the officer who testified against him with respect to the purpose of the transfer of drug cases to a special unit of which the officer was a member, and generally on the question whether "political pressures required him to artifically create a substantial increase in drug convictions." Id. at 219. The prosecutor objected on the ground that the proposed line of inquiry would convert the case into a "political trial," and the trial judge sustained the objection. With obvious reluctance, the Supreme Court of North Dakota affirmed Bartkowski's conviction:
Although we probably would not have limited the cross-examination in the manner that the trial court did, that is not the standard we apply in our review. Ordinarily it is preferable that trial courts permit overextended cross-examination rather than imposing limitations which may be unnecessary.... Considering the rule that one who cross-examines on an irrelevant matter is bound by the answer he receives, it is doubtful that this case would have become a political trial if Kemmet would have been permitted to answer the questions that were objected to. There is no reason to believe, and the offer of proof made no claim, that Kemmet would have admitted that, in effect, he had "framed" Bartkowski in order to build up impressive statistics in the drug law enforcement program. We cannot say, under the circumstances here, that the trial court's limitation of cross-examination was an abuse of discretion.
Id. at 219-220. The court, implicitly differing with a contrary statement in Haeger, supra, specifically noted that Davis v. Alaska, supra, was not inconsistent with its conclusion. Id. at 220.
In Rowe v. State, 62 Md.App. 486, 490 A.2d 278, cert. denied, 303 Md. 684, 496 A.2d 683 (1985), the defendant in a first-degree murder prosecution requested leave to ask the investigating officer on cross-examination whether promotions were awarded for closing out major homicides. The trial judge sustained the prosecutor's objection, and the appellate court affirmed. The court stated that
the "promotion" question was general in nature, could have had no special bearing on the credibility or bias of the witness and seemingly was proposed to create prejudice against police in general. Policemen, we assume, like other employees, secure advancement through the performance of good work. There is nothing inherently inappropriate in that universally accepted practice. The question as articulated by defense counsel did not focus upon any specific personal bias on the part of Detective Tankersley which might have been motivated by a promise of promotion for closing out this particular case.
A "common thread" emerges from those cases where cross-examination to show bias is at issue: the cross-examination must be designed to elicit a specific personal bias on the part of the witness.
Id. at 497-98, 490 A.2d at 283-84 (emphasis in original) (footnote omitted). The court distinguished Haeger, supra, on the ground that
in Haeger not only was the quota pressure directed to the arresting officer but the entire state's case rested on the credibility of the officer.
Id. at 498-99, 490 A.2d at 284 (emphasis in original).

IV
If a lawyer asks a witness a question which contains an assertion of fact, you may not consider the assertion as evidence of that fact. The lawyer's statements are not evidence.
CRIMINAL JURY INSTRUCTIONS FOR THE DISTRICT OF COLUMBIA No. 1.04 (3d ed. 1978). Practically every jury which sits in the District of Columbia hears this instruction at least once during the course of a trial. Jurors are presumed to follow the instructions *1087 of the court, but after a skunk has been thrown into the jury room, it is too late to instruct the jury not to smell it. See Thompson v. United States, 546 A.2d 414, 425 (D.C.1988). Once the idea that a large number of arrests will lead to promotion has been planted in the jurors' minds, one might as well order them not to think about a pink elephant. Perhaps they can follow such a directive. Perhaps not. Cf. Scull, supra, 564 A.2d at 1164, and cases there cited.
In the questionable character of the proposition that jurors can forget, or at least ignore, the unforgettable lies the danger of the kind of cross-examination which counsel for Van Ness proposed to pursue in this case. Once the question whether officers are promoted, in part, on the basis of the number of arrests they make has been posed, it may be difficult even for the most conscientious juror not to muse on the subject, no matter what the officer's answer may be. Under these circumstances, trial judges should surely be reasonably exacting in requiring counsel to establish a good faith basis for pursuing such a line of inquiry. See Jones v. United States, 516 A.2d 513, 517 (D.C.1986); United States v. Fowler, 151 U.S.App.D.C. 79, 81, 465 F.2d 664, 666 (1972). It would not suffice, for example, if counsel relied on a tip from a client or witness to the effect that, according to the talk on the street, officers are promoted more rapidly if they make lots of arrests.
In the present case, however, defense counsel proffered that another vice officer from the same police district as Officer Thompson had admitted, while testifying in another case, that "one of the bases for evaluation is whether arrests are made on the basis of [officers'] undercover operations." In my opinion, these are "`facts which support a genuine belief' that the witness is biased in the manner asserted." Jones, supra, 516 A.2d at 517 (quoting Fowler, supra, 151 U.S.App.D.C. at 81, 465 F.2d at 666). The judge might reasonably have asked to see the transcript or hear the tape of the other officer's testimony, in order to satisfy himself as to exactly what the other officer had said. The accuracy of counsel's representation to the court was not challenged, however, and I think the proffer was more than sufficient.
Given a good faith basis for the proposed line of inquiry, I find the decisions in Bartkowski and Haeger, which encourage (Bartkowski) or require (Haeger) the trial judge to permit counsel to explore any connection between arrests and evaluations, to be more persuasive than decisions which go the other way. In Baril and Williamson, trial court rulings sustaining prosecutors' objections were affirmed with little or no discussion of the issue here presented.[2] In Rowe, the court appeared to require a showing not only that officers as a group could gain from the early closing of homicide cases, but also that the witness had some specific personal bias beyond the incentive common to all members of the group. I find this distinction analytically flawed; if the witness had a motive to cut corners or to be careless with the truth, it is surely irrelevant whether other persons were also subject to the same temptation.
Although the North Dakota court in Bartkowski and the Indiana court in Haeger were both troubled by their respective trial courts' restriction of cross-examination, they reached different results. In Bartkowski, the court sent a message to trial judges that greater liberality would be appropriate in the next case, but in the final analysis declined to find an abuse of discretion. In Haeger, on the other hand, the court held that the restriction on cross-examination required reversal of the defendant's conviction, especially since the government's entire case, including the results of the breathalyzer test, hinged on the officer's credibility. Although the Haeger approach has some appeal  for one thing, it gives trial judges an unequivocal directive and does not leave them guessing as to what we might say or do in the next case  I think it more prudent to follow *1088 Bartkowski, at least to the extent of leaving the issue generally to the trial court's discretion.[3] I would elaborate on or modify the Bartkowski approach, however, and hold that the trial judge should presumptively permit such questioning unless he or she affirmatively concludes, on the basis of the circumstances of the particular case, that the prejudicial impact of the inquiry would outweigh its probative value.

V
My colleagues suggest that the proscription of counsel's cross-examination on the connection between the officer's evaluation and the number of arrests which he generates was a proper exercise of discretion because the defense was permitted to ask other questions relevant to bias. They note that the defense brought out the fact  a chilling one to me  that Officer Thompson first told the grand jury that $50 in pre-recorded currency had been recovered from Van Ness (and then amended his testimony to say that it was $5) when in fact no such funds had been found on him, and $5, not $50, had been found on someone else.[4] They also point to the fact that Officer Thompson was asked if Operation Clean Sweep was designed to achieve as many drug arrests as possible.[5] Impeachment for bias having occurred, says the majority, we have here only the question of the scope of the inquiry, a matter confided to the trial judge's discretion.
I do not agree. Officer Thompson's untrue grand jury testimony does not necessarily show bias; a mistake is consistent with impartiality. The existence of an incentive to arrest as many people as possible, and to make the arrests stick, however, might well shed light on the issue whether the officer was deliberately lying, reckless with the truth, or merely mistaken. Nor was the limited inquiry which was permitted into Operation Clean Sweep directly related to bias. The obvious fact that a major police operation against drug sellers and abusers is designed to arrest violators does not provide the same kind of incentive to lie, or at least to be careless with the truth, as does the prospect that an officer can gain professionally (and ultimately financially) from the number of arrests which he or she makes or brings about.
Even assuming that an officer would not deliberately make a false identification just to add another arrest to his total and thus enhance his opportunity for promotion  and such an assumption is surely a reasonable one with respect to most officers in this jurisdiction[6]  the incentive created by a policy linking the number of arrests to prospects on the job would nevertheless be relevant to the officer's credibility. There are many shades of gray between the extremes of black and white. Experience teaches us that we often believe what we want to believe. If the officer's professional advancement would be enhanced if Van Ness were the right man, would this not make him, at least subconsciously, more inclined to be certain of his identification than he would be if the incentive did not exist? A judicial officer must be disqualified from presiding at a trial if he has any financial stake in the defendant's conviction. Tumey v. Ohio, 273 U.S. 510, 532, 47 S.Ct. 437, 444, 71 L.Ed. 749 (1927); see also Scott v. United States, 559 A.2d 745, 748-50 (D.C.1989) (en banc). A policeman is not a judicial officer, and he would obviously not be disqualified from testifying if such an incentive existed. Nevertheless, if *1089 he has such a stake in the outcome, the jurors should surely know of it.[7]
In addition, in the present case, the trial judge refused to permit the proposed questioning despite the lack of an objection by the prosecutor. The judge made no explicit finding as to how the government would be prejudiced, confining himself to the comment that his ruling would avoid problems later on. Under these circumstances, it is my opinion that the judge did not adequately justify his ruling that the proposed cross-examination should be proscribed.

VI
Improper denial of the opportunity to cross-examine for bias is subject to the harmless error analysis set forth in Chapman v. California, 386 U.S. 18, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967). "The correct inquiry is whether, assuming that the damaging potential of the cross-examination were fully realized, a reviewing court might nonetheless say that the error was harmless beyond a reasonable doubt." Van Arsdall, supra, 475 U.S. at 684, 106 S.Ct. at 1438.[8]
The analysis set forth in Van Arsdall provides a useful framework in which to analyze the impact of the trial court's denial of cross-examination on the issue under discussion. The Supreme Court there held that the factors to be considered "include the importance of the witness' testimony in the prosecution's case, whether the testimony was cumulative, the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points, the extent of cross-examination otherwise permitted, and, of course, the overall strength of the prosecution's case." 475 U.S. at 684, 106 S.Ct. at 1438. See also Brooks v. United States, 516 A.2d 913, 916 (D.C.1986).
Application of the first factor  "the importance of the witness' testimony in the prosecution's case"  to the present record supports a finding that the error was prejudicial rather than harmless. As in Olden v. Kentucky, ___ U.S. ___, 109 S.Ct. 480, 484, 102 L.Ed.2d 513 (1988), Thompson's testimony was "central, indeed crucial, to the prosecution's case." "The opportunity to present evidence of bias becomes particularly important when, as here, the credibility of a key government witness is the central issue." Benjamin v. United States, 453 A.2d 810, 811 (D.C.1982); see also Wynn v. United States, 130 U.S.App. D.C. 60, 63, 397 F.2d 621, 624 (1967), in which the trial court's refusal to allow cross-examination of the government's "star witness" for bias was held to be reversible error. Officer Thompson was the sole eyewitness to the transaction and the only one who identified Van Ness as a participant. For all practical purposes, Officer Thompson was the government's case.
As the government candidly acknowledges in its brief, Officer Thompson's testimony was not cumulative, nor was it significantly corroborated by other witnesses.[9]*1090 None of the other government witnesses claimed any personal knowledge of the sale or of the role which Van Ness was said to have played in it. Indeed, Officer Thompson was the only witness who identified Mr. Van Ness as having participated in the transaction at all.
The third factor  "the presence or absence of evidence corroborating or contradicting the testimony of the witness on material points"  also highlights the prejudice resulting from the restriction of cross-examination in this case. There was no physical evidence connecting Van Ness with the sale. Although he was arrested a short time after the transaction, the arresting officer did not find pre-recorded funds or drugs on him. See Coligan v. United States, 434 A.2d 483, 485 (D.C.1981), holding that where the key government witness' "largely uncorroborated testimony establishes one or more elements of the charge," cross-examination for bias is especially important, and Springer, supra, 388 A.2d at 855, holding that cross-examination is particularly significant where the testimony "has little independent corroboration."
A more difficult question is whether "the extent of cross-examination otherwise permitted," Van Arsdall, supra, 475 U.S. at 684, 106 S.Ct. at 1438, rendered the restriction imposed by the judge harmless. As I have noted above, the defense was permitted to question Officer Thompson about his incorrect (or worse) testimony before the grand jury and about the nature and purposes of Operation Clean Sweep. Defense counsel also brought out alleged errors in the officer's "buy report," as well as the fact that an undercover officer necessarily engages in some deception when he represents himself to be a buyer of unlawful drugs rather than a "law man" bent on apprehending wrongdoers. In my opinion, however, these subjects, while relevant to Officer Thompson's credibility, do not necessarily show bias. While they go to the accuracy of his testimony, they do not provide a motive to lie, or to believe what one wishes to believe, in order to promote one's own prospects for a favorable evaluation. If Officer Thompson could further his professional advancement by generating large numbers of arrests, then the jury might well conclude that the errors in his testimony were not inadvertent but deliberate, or at least that he believed what it was in his interest to believe.[10]
Finally, Van Arsdall requires us to consider "the overall strength of the prosecution's case." Officer Thompson certainly had an adequate opportunity to view Van Ness, and this would ordinarily make the case against the defendant a strong one. Nevertheless, in light of the lack of corroboration of his testimony and the serious errors which the officer was shown to have made, the government's case was less than overwhelming. Its strength (or weakness) depended entirely on the credibility of the witness as to whom cross-examination was improperly restricted. Cf. Thomas v. United States, 557 A.2d 1296, 1303 (D.C. 1989) (closeness of case difficult to assess where question turns on defendant's credibility).
Officer Thompson's credibility was the central issue in this case. His competence was subjected to persuasive challenge by the exposure of apparent deviations from proper police procedures in the preparation *1091 of his buy report. His reliability was potentially undermined by the revelation that he had informed the grand jury that pre-recorded funds had been found on Van Ness when this was entirely untrue. What was lacking, however, was something to tie this all together, to provide a reason for the sloppiness and the untrue testimony. Disclosure of what Officer Thompson allegedly stood to gain professionally from causing Van Ness and others to be arrested might well have provided the missing link for the jury. As this court has recognized, "[t]he exposure of bias or partiality as a motivational factor may be even more damaging to the value of a witness' testimony than a more generalized credibility attack." Springer, supra, 388 A.2d at 855; see also In re C.B.N., 499 A.2d 1215, 1221 (D.C. 1985). If the jurors learned of an economic or professional incentive for Officer Thompson to bring about an arrest, they might well have concluded that he would be, at least, less cautious about identifying the right man, for self-interest can assuredly cloud one's judgment.
I recognize that this is a close case, that retrials have substantial societal costs, Scott v. United States, supra, 559 A.2d at 766 (concurring opinion), and that while fairness is required in criminal trials, perfection is not. See Dixon v. United States, 565 A.2d 72, 81 (D.C.1989). Maintaining a sense of proportion is important when judges decide whether to reverse a conviction for some real or perceived error or imperfection in the proceedings. It may very well be that the result of this trial would have been the same even if Van Ness had been permitted to proceed with the proscribed inquiries on cross-examination. Officer Thompson's answer to the question whether his mission in Operation Clean Sweep was to make as many arrests as possible  "I don't know"  raises some doubt as to whether he would have given the defense a helpful answer[11] to the question whether favorable evaluations are based in part on numbers of arrests generated. I cannot conclude, however, that the judge's ruling, which I believe to have been erroneous, was harmless beyond a reasonable doubt. Accordingly, I would reverse the conviction and remand for a new trial.[12]
NOTES
[1]  This is not accurate as there was cross-examination on the matter of Police Department policy to a limited degree, as will appear.
[1]  The court thought the following language in Springer, supra, 388 A.2d at 856, applicable to the question before it:

Where the record reflects a curtailment of a requested line of bias cross-examination in limine, so that the jury is unable properly to perform its fact-finding function in inferring bias from the testimony as a whole, we will assess cross-examination errors by a per se error standard.
[2]  I am unpersuaded by the notion of the court in Baril that the possible self-interest of the officer in securing promotion is too "foreign" to the determination of the speed at which the defendant was travelling. Bias is rarely if ever remote. See Scull, supra, 564 A.2d at 1165.
[3]  For factors that would guide this discretion, see part V of this opinion, infra.
[4]  This kind of thing happens much too often. See, e.g., Sanders v. United States, 550 A.2d 343, 347 (D.C.1988) (concurring opinion) (officer's "mistaken" testimony to grand jury about positive paraffin test which supposedly implicated defendant); Wilson v. United States, 558 A.2d 1135, 1137 n. 1 (D.C.1989) (officer's false statement in affidavit in support of arrest warrant that witness had identified defendant).
[5]  The officer testified that the purpose of the operation was to make drug arrests, but the examination continued as follows:

Q. Any part of your mission, as part of Operation Clean Sweep, was to make as many drug arrests as you could, isn't that correct?
A. I dont' know.
[6]  But not necessarily all officers. See note 4, supra.
[7]  The point I am making is well illustrated in an incident related by one of history's most astute and eloquent observers of human nature, the "Bard of Stratford on Avon." King Henry IV, who is gravely ill, is asleep on his bed. His son, Prince Hal (later King Henry V) comes to his bedside and persuades himself that his father's sleep is permanent  "a sleep that from this golden rigol hath divorced so many English kings." He takes the crown, places it on his head, and departs. The king awakes, learns what has occurred, and summons his son. The exchange when a thoroughly chastened and embarrassed Prine Hal returns is revealing:

PRINCE: I never thought to hear you speak again.
KING: Thy wish was father, Harry to that thought. I stay too long by thee. I weary thee.
W. SHAKESPEARE, HENRY IV, Part 2, Act 4, Scene 5, lines 90-92.
If a jury were asked to assess a report by Prince Hal that the king has died, could it make an informed determination if it did not know of his stake in the matter? I believe that the difference between that case and the present controversy is one of degree, not of kind.
[8]  The government acknowledges in its brief that if the restriction on cross-examination was improper, the question which we must decide is whether the error was harmless beyond a reasonable doubt.
[9]  The lookout radioed by Officer Thompson provides a measure of corroboration for his testimony. The lookout was, however, somewhat general in its content. Indeed, within a few minutes of Officer Thompson's broadcast, the two arrest teams stopped two different men  Grant and Van Ness  apparently concluding that each of them fit the description of one of the suspects. Moreover, the clothing worn by Van Ness did not precisely match the lookout.
[10]  This case is distinguishable from authorities cited by the government in which cross-examination as to bias was only marginally restricted. In Beynum v. United States, 480 A.2d 698, 706-08 & n. 21 (D.C.1984), for example, the jury "was aware of sufficient facts, and heard sufficient testimony from which it could infer (and from which defense counsel could argue) bias," id. at 707, namely, that the testifying officer could have job difficulties if he fired his weapon improperly. Id. In Rhodes v. United States, 354 A.2d 863, 866 (D.C.1976), this court held that the denial of cross-examination into federal narcotics charges pending against the complaining witness, although erroneous, was harmless, in part because "[a]ppellant was permitted to cross-examine [the witness] extensively regarding his possession of narcotics paraphernalia and his possession and use of marijuana and cocaine on the date of the robbery."
[11]  A witness' professed ignorance of a subject about which one might expect him to know may, of course, be helpful to his adversary.
[12]  I agree with my colleagues that there was no trial court error in relation to appellant's alleged use of an alias.
