
745 A.2d 274 (2000)
James O. GRAYTON, Appellant,
v.
UNITED STATES, Appellee.
No. 96-CF-1393.
District of Columbia Court of Appeals.
Argued November 10, 1998.
Decided February 3, 2000.
*276 Daniel K. Dorsey, Washington, DC, appointed by the court, for appellant.
Barton S. Aronson, Assistant United States Attorney, for appellee. Wilma A. Lewis, United States Attorney, and John R. Fisher, Thomas J. Tourish, Jr., Amy J. Conway, and Robin C. Ashton, Assistant United States Attorneys, were on the brief for appellee.
Before TERRY and RUIZ, Associate Judges, and NEWMAN, Senior Judge.
TERRY, Associate Judge:
In the early morning hours of May 30, 1994, a bed in the apartment of Margaret Jenkins was set ablaze. Jenkins' estranged boy friend, appellant Grayton, was arrested and charged with second-degree burglary,[1] arson,[2] destruction of property,[3]*277 and threats to injure another person.[4] After a jury trial, he was convicted on all counts. On appeal, Grayton claims that the trial court committed reversible error by restricting the scope of his cross-examination of Ms. Jenkins about her alleged prior drug use and by refusing to allow him to introduce extrinsic evidence of that drug use. Grayton also contends that the trial court erred in allowing the government to present evidence that he had been seen carrying a gasoline can shortly before the fire occurred and in permitting the government to cross-examine his parents about their knowledge of his whereabouts on the night of the fire. We reject all of these arguments and affirm the judgment of conviction.

I

A. The Government's Evidence

Early in 1994 James Grayton became romantically involved with Margaret Jenkins. Sometime in February he moved into her two-bedroom basement apartment on Maryland Avenue, N.E., after she gave him a key to the front door. Their relationship, however, was a stormy one, marked by frequent quarreling. In mid-May, after a heated argument, Ms. Jenkins called the police and had Grayton evicted from her apartment.
At about 8:00 p.m. on May 29, Ms. Jenkins was walking home from work when she encountered Grayton on the street near her home. An argument ensued, and Jenkins threatened to call the police if Grayton did not leave her alone. Grayton left, but warned Jenkins that he would return.
Later that night, Ms. Jenkins and William Smith, her former boy friend, were confronted by Grayton when they returned to Jenkins' apartment after a trip to the liquor store. Grayton angrily accused Jenkins of kicking him out of her apartment so that she could get back together with Smith. He then shoved Jenkins and made a motion as if to hit her. Turning to Smith, he threatened to "fuck [Smith] up" and "kill [his] ass" if he did not leave Jenkins alone. When Jenkins walked across the street to a telephone booth in order to call the police, Grayton followed and grabbed the phone out of her hand. He said he would "fuck [them] both up if he [caught them] together again." Smith and Jenkins then went into a restaurant to call the police, but they were asked to leave after Grayton followed them in and acted "like he wanted to fight." Back outside, Grayton said, "I'm going around to get my boys and I'm going to fuck you up." He then departed.
Smith and Jenkins went back to Smith's apartment. They were sitting in the front yard, inside the gate that separated the yard from the sidewalk, having a drink with their friend Robin Anderson when Grayton returned and again confronted them. When Jenkins asked Smith to come inside with her while she changed clothes, Grayton warned, "If you go down there, it's going to be a burning bed. You mother fuckers will not come out of there alive." He also said, "I promised you I was going to give you the burning bed"[5] and "I promise you this, neither one of you mother fuckers will sleep in this house tonight, you can bet on that." Ms. Jenkins then went inside alone to change clothes. When she returned after a few minutes, Jenkins, Smith, and Anderson drove away in Smith's car.
Later that evening, at 11:02 p.m., Ms. Jenkins called 911 to complain about Grayton's harassment. During the call, Grayton stood directly behind her, warning her that she had "better not call the police." When half an hour passed with no response from the police, Jenkins called 911 again, at 11:32 p.m. This time she told the dispatcher that Grayton had chased her *278 around the corner and that she wanted him removed from her house. Grayton remained in Jenkins' front yard, angrily shouting that "nobody [was] sleeping in that house that night, nobody." Forty-five minutes later, at 12:15 a.m., Ms. Jenkins called 911 for the third time. Hoping to increase the likelihood that the police would actually respond, she told the dispatcher that Grayton had guns and knives and had threatened to shoot her. Another half-hour passed, and still the police did not come. At 12:43 a.m. Jenkins once again called 911, this time from a phone booth on the corner. She told the dispatcher that Grayton was in her apartment and had locked her out, and that she was going to get a gun and kill him.
Shortly after 1:00 a.m. the police finally arrived. Jenkins told them she wanted Grayton out of her apartment. Before they would act on this request, they told her that she had to pack up the remainder of his belongings in order to prove to them that she was serious. Jenkins proceeded to gather up Grayton's belongings and place them outside. As she did so, Grayton declared, "I'll be back. This ain't going to stop me." The police escorted him outside the fence, warned him that he would be arrested if he re-entered the front yard, and then left.
Grayton proceeded to a nearby liquor store, where he met his friend Jason Postell. Grayton asked Postell whether he had a gasoline can. When Postell replied that he did not, Grayton said he was "going up the street to see if he could get one." Some time later, Ethan King, who lived across the street from Ms. Jenkins, saw Grayton walking through the neighborhood carrying what appeared to be a plastic gasoline can.
In the meantime, Ms. Jenkins and Mr. Smith went to an after-hours club for drinks, where they remained for about forty-five minutes. After they left the club and were walking near 14th and G Streets, N.E., a short distance from Jenkins' apartment, they both saw Grayton across the street, walking in the opposite direction. Jenkins grew nervous and began to run towards her apartment. She opened the door to find the apartment in flames.[6] Ms. Jenkins immediately ran across the street to find a phone and report the fire. This fifth and final 911 call was made at 3:30 a.m.
According to Adam Young, Jr., an investigator with the District of Columbia Fire Department, the fire originated in Jenkins' bed and burned for approximately thirty minutes. There was nothing to indicate that an accelerant had been used to start the fire, nor was there any evidence that the fire was the result of either smoking or drug use. Although both Smith and Jenkins were smokers, Smith never entered Jenkins' apartment that night, and Jenkins testified that she did not smoke inside the apartment. Detective Carl Webster, a fire investigator with the Metropolitan Police Arson Strike Team, also testified that the fire was confined to the bed. In his opinion, the fire was started by someone holding a match or a cigarette lighter to bed linen or clothing.[7]
About two days later, Grayton confessed to Postell that he had started the fire.

B. The Defense Evidence

Three witnesses testified in support of Grayton's alibi defense. His parents, Willa and David Grayton, said that he came to their house at about 12:30 or 1:00 a.m. on the night of the fire and asked if he could leave his clothes with them. A short time *279 later, he returned with his friend Gary Thomas, took some clothes down to the basement, and stayed there. David Grayton testified that he saw his son in the basement at 3:00 or 3:30 a.m., and again at 4:45 a.m. Willa Grayton also said she saw him in the basement at 4:45 a.m. Gary Thomas stated that he remained with Grayton until sometime between 4:30 and 5:00 a.m.
Grayton also called Timothy May, a former police officer and state fire marshal in Maryland, as an expert in fire investigation. May agreed with the government's experts that the fire was confined to the bed and that it burned for less than half an hour. He said, however, that the cause of the fire could not be determined, and specifically stated that cigarette smoking could not be ruled out.

C. The Government's Rebuttal

Ms. Jenkins testified that immediately after she called the fire department at 3:30 a.m., she telephoned Mr. and Mrs. Grayton and told them that their son had just set fire to her apartment. Mrs. Grayton asked Jenkins if she knew where Grayton was. About ten minutes later, Grayton's parents arrived at Jenkins' home. Again they asked Jenkins if she knew their son's whereabouts and said that they would go and look for him.

II

A. Cross-examination of Margaret Jenkins

During his cross-examination of Ms. Jenkins, defense counsel brought out the fact that she had previously been convicted of conspiracy to possess cocaine with the intent to distribute it. Counsel then asked whether she had been using cocaine on the night of the fire. The court sustained the government's objection to this question on the ground that it implied a relation between the prior conviction in 1987 and Jenkins' behavior in 1994. Now, on appeal, Grayton argues that this line of cross-examination would have demonstrated that Jenkins herself started the fire by smoking crack cocaine in her apartment that night. That, in turn, would show that her testimony against Grayton was biased  specifically, that it was motivated by a desire to cover up her own responsibility for the fire. Grayton contends that the trial court's refusal to allow this line of questioning violated his rights under the Confrontation Clause of the Sixth Amendment. He also maintains that, even if there was no constitutional violation, the court abused its discretion, see (James) Johnson v. United States, 398 A.2d 354, 361-363 (D.C.1979), and thus he must be granted a new trial.
"A defendant's Sixth Amendment right to confront adverse witnesses necessarily includes the right to cross-examine." Ray v. United States, 620 A.2d 860, 862 (D.C.1993) (citations omitted). Moreover, "the exposure of a witness' motivation in testifying is a proper and important function of the constitutionally protected right of cross-examination." Davis v. Alaska, 415 U.S. 308, 317, 94 S.Ct. 1105, 39 L.Ed.2d 347 (1974). Thus the bias or partiality of a witness is "always a proper subject of cross-examination." Hyman v. United States, 342 A.2d 43, 44 (D.C.1975) (citing Davis).
The Confrontation Clause is violated, however, only when the trial court precludes "a `meaningful' degree of cross-examination" to establish bias. Flores v. United States, 698 A.2d 474, 479 (D.C. 1997) (citation omitted); see Springer v. United States, 388 A.2d 846, 854 (D.C. 1978) ("Some meaningful degree of cross-examination must be allowed in the first instance" to satisfy the Sixth Amendment). Thus we must determine whether defense counsel had a sufficient opportunity on cross-examination to "bring out considerations relevant to motive or bias." (Irving) Johnson v. United States, 418 A.2d 136, 140 (D.C.1980) (citations omitted); see, e.g., Elliott v. United States, 633 A.2d 27, 33 (D.C.1993). At the same time, of *280 course, we must bear in mind that "[t]here is no constitutional right to present irrelevant evidence." Gibson v. United States, 536 A.2d 78, 82 (D.C.1987).
In order to cross-examine a witness about a prior bad act that has not resulted in a criminal conviction, the examiner (1) must have a factual predicate for asking the question and (2) must show that the act "`bears directly upon the veracity of the witness in respect to the issues involved [in] the trial.'" Sherer v. United States, 470 A.2d 732, 738 (D.C.1983) (citations omitted), cert. denied, 469 U.S. 931, 105 S.Ct. 325, 83 L.Ed.2d 262 (1984); accord, e.g., Winfield v. United States, 676 A.2d 1, 4 (D.C.1996) (en banc); Murphy v. Bonanno, 663 A.2d 505, 508-509 (D.C. 1995); Kitchen v. United States, 95 U.S.App. D.C. 277, 279, 221 F.2d 832, 834 (1955). This two-part standard "constitutes a minimum threshold for the admissibility of proposed cross-examination into alleged prior bad acts, and evidence which fails to satisfy the Sherer test may not be admitted." Roundtree v. United States, 581 A.2d 315, 323 (D.C.1990).
To meet the first requirement under Sherer, "the questioner must proffer `some facts which support a genuine belief' that the witness is biased in the manner asserted." Jones v. United States, 516 A.2d 513, 517 (D.C.1986) (citations omitted); see Ray, 620 A.2d at 862-863; (Irving) Johnson, 418 A.2d at 140. "[T]he 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." Scull v. United States, 564 A.2d 1161, 1164 n. 4 (D.C.1989).
Grayton fails to satisfy the first prong of the Sherer test. The only basis for his theory that Ms. Jenkins might have started the fire by smoking crack in her apartment was the fact that she had smoked crack before. He could offer no evidence that she had done so on the night in question, and in fact all of the evidence at trial indicated otherwise. Defense counsel did make a proffer that Robin Anderson would testify that she and Jenkins had been smoking crack cocaine on the night of the fire, at about 1:30 a.m., and the court ruled that such testimony would be admissible. Later, however, when counsel began his examination of Anderson, he reverted to asking the question much more generally, without tying it to the time and place of the fire. At that point the court properly stopped the questioning.[8]
The trial court nevertheless did err in one respect, but we conclude that the error was harmless. At the time the court sustained the government's objection to defense counsel's proposed cross-examination of Ms. Jenkins, Ms. Anderson had not yet testified, but counsel had made a proffer of her testimony. Specifically, counsel had proffered that Anderson would testify that she and Jenkins had smoked crack that same night, shortly before the fire began. Given this proffer, the court erred in precluding cross-examination of Jenkins about smoking crack cocaine on the night of the fire before it knew that Anderson's testimony would not live up to the proffer. However, the fact that Anderson did not testify as counsel had proffered renders any error harmless under Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), especially in light of the strong evidence of guilt.
We turn to Grayton's alternative argument that the trial court abused its discretion in sustaining the government's objection to his question. It is well settled that, despite the Sixth Amendment, *281 the trial court has broad discretion "to `impose reasonable limits' on cross-examination `based on concerns about, among other things, harassment, prejudice, confusion of the issues, the witness' safety, or interrogation that is repetitive or only marginally relevant.'" Roundtree, 581 A.2d at 323 (quoting Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986)); accord, Elliott, 633 A.2d at 32 (citing Roundtree); Scull, 564 A.2d at 1164. A proposed line of questioning may, and should, be disallowed if the trial court concludes that its probative value is substantially outweighed by the danger of unfair prejudice. Roundtree, 581 A.2d at 323.
In this case, the probative value of the proposed cross-examination was minimal, and the risk of prejudice was considerable. There was a substantial danger that this line of inquiry would distract the jury from the issue of Grayton's guilt or innocence, causing it to focus instead on the collateral issue of Jenkins' alleged drug habit. Moreover, defense counsel was not totally prevented from cross-examining Jenkins in an effort to show possible bias, and indeed he did so. The trial court merely prevented counsel from introducing an irrelevant, collateral, and potentially prejudicial issue into the trial. On the record before us, we can find no abuse of discretion.

B. Extrinsic evidence of prior drug use

Grayton also challenges the trial court's restrictions on his attempts to introduce extrinsic evidence of Ms. Jenkins' drug use. First, he argues that, under the Sixth Amendment, this evidence should have been admitted to support his theory that Jenkins was biased. In addition, he contends that the exclusion of this evidence violated his due process right to present exculpatory evidence of a third-party perpetrator. Because the same standard governs the admissibility of such evidence for either purpose, we shall address these arguments together.
Defense counsel called Robin Anderson as a witness and sought to ask her about Ms. Jenkins' prior drug use. When the government objected, the trial judge ruled that the questions were irrelevant and limited defense counsel to asking whether Jenkins smoked crack cocaine in the apartment on the night in question, in the hours immediately preceding the fire. Counsel elected not to pursue his line of inquiry under these restrictions.
Later, just before the testimony of Mr. May, the defense expert on fires, the judge asked defense counsel, "You're not going to ask him questions predicated on crack cocaine, are you?" Counsel replied, "No, I'm not." The judge then cautioned defense counsel, "I would hope the words `crack cocaine' don't come out of your mouth ... because you're flirting with contempt, as it is." Counsel never attempted to ask Mr. May any questions relating to crack cocaine, but he was able to elicit a statement that smoking could not be ruled out as a cause of the fire.
Grayton certainly had the right to challenge the credibility of Ms. Jenkins by offering extrinsic evidence to show bias. Bassil v. United States, 517 A.2d 714, 716-717 (D.C.1986); In re C.B.N., 499 A.2d 1215, 1218 (D.C.1985); (Irving) Johnson, 418 A.2d at 140; see United States v. Abel, 469 U.S. 45, 52-55, 105 S.Ct. 465, 83 L.Ed.2d 450 (1984). Additionally, a defendant's constitutional right to present exculpatory evidence in his own defense includes "the right to present evidence that someone else committed the offense for which the defendant is on trial." Elliott, 633 A.2d at 32.
These rights, however, are subject to the trial court's discretion to exclude evidence for lack of relevance. Winfield, 676 A.2d at 4; Gibson, 536 A.2d at 81. "Relevant evidence is that which tends to make the existence or nonexistence of a fact more or less probable than would be the case without that evidence." Punch v. United States, 377 A.2d 1353, *282 1358 (D.C.1977), cert. denied, 435 U.S. 955, 98 S.Ct. 1586, 55 L.Ed.2d 806 (1978). In the present context, this requires "proof of facts or circumstances which tend to indicate some reasonable possibility that a person other than the defendant committed the charged offense." (Woredell) Johnson v. United States, 552 A.2d 513, 516 (D.C.1989), adopted en banc in Winfield, 676 A.2d at 4. "The `focus' of the standard is not on the third party's guilt or innocence, but on `the effect the evidence has upon the defendant's culpability,' and in this regard it `need only tend to create a reasonable doubt that the defendant committed the offense.'" Winfield, 676 A.2d at 4 (quoting (Woredell) Johnson, 552 A.2d at 517 (emphasis in Johnson)).
The proposed evidence of Ms. Jenkins' prior use of cocaine does not even meet this relatively low threshold. A trial judge should exclude "evidence that `is too remote in time and place, completely unrelated or irrelevant to the offense charged, or too speculative with respect to the third party's guilt.'" Winfield, 676 A.2d at 5 (quoting (Woredell) Johnson, 552 A.2d at 516). In Robinson v. United States, 642 A.2d 1306, 1310 (D.C.1994), this court held that evidence of a witness' use of alcohol several years earlier was "plainly irrelevant" and collateral to the question of whether she might have been intoxicated on the night of the crime. In this case the same is true of the proposed evidence of Jenkins' past use of crack cocaine. There was no evidence whatever that Ms. Jenkins was using cocaine on the night of the fire; thus the proposed questioning about her past drug use was at least as irrelevant as the corresponding questions in Robinson.
Even if we were to assume that evidence of Jenkins' past behavior made it more likely that she smoked crack that night, the defense could still offer nothing beyond mere speculation that such smoking was the cause of the fire. Given the testimony of the fire investigators that no matches, lighters, drug paraphernalia, or ashtrays were found in Jenkins' bedroom after the fire, there was no corroborative evidence to support the defense theory. Moreover, this court has "repeatedly emphasized [that] the determination that evidence is relevant does not exhaust the trial judge's responsibility in deciding whether to admit it. The judge must also balance the probative value of the evidence `against the risk of prejudicial impact.'" Winfield, 676 A.2d at 5 (citation omitted). The trial judge thus retains discretion "to exclude marginally relevant evidence creating the danger that ... [it] will distract the jury from the issue in this case." Id. On this record we discern no abuse of that discretion.
For all of these reasons, we find no basis for reversal in the trial court's refusal to allow the defense to present extrinsic evidence of Ms. Jenkins' prior drug use.

C. Evidence of Grayton's search for gasoline

Grayton maintains that the government should not have been allowed to introduce evidence that he was seen carrying a gasoline can near Ms. Jenkins' apartment shortly before the fire occurred and that he asked De Lante Adams, Jenkins' neighbor, for some gasoline. He asserts that this evidence was offered to show that he had a "predisposition to commit the crime," and that it was prejudicial and irrelevant because the government's theory of the case was inconsistent with any inference that gasoline was used to start the fire.
This argument is without merit. First, one of the government's experts, Detective Webster, testified that "maybe a small amount" of accelerant, such as gasoline, might have been used to start the fire (see note 7, supra). More importantly, evidence that Grayton attempted to find a source of gasoline on the night in question was clearly relevant to his intent to start a fire in Jenkins' apartment, regardless of whether gasoline was actually used. See Williams v. United States, 283 A.2d 212, *283 213 (D.C.1971) (defendant's possession of a quart bottle containing gasoline, wrapped in a coat, along with "a book of matches with the cover torn off," was sufficient in context to prove intent to burn a building even though no fire actually occurred); cf. United States v. Brooks, 146 U.S.App. D.C. 1, 8-9, 449 F.2d 1077, 1084-1085 (1971) (fact that murder defendant brought a shotgun to the scene of the crime was admissible to show premeditation, even though the crime was actually committed with a knife). Contrary to Grayton's argument, the government's theory of the case was not dependent on whether he used gasoline to start the fire. In fact, Detective Webster testified that the fire was most likely started by someone holding an open flame to the bed linens or to clothing on the bed.
We therefore hold that the admission of evidence concerning the gasoline can was not reversible error. In light of Williams and Brooks, we are satisfied that the evidence was properly admitted; but even if it was not, its admission was surely harmless, given the strength of the government's case. See Kotteakos v. United States, 328 U.S. 750, 764-765, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946).

D. Cross-examination of Grayton's parents

Grayton claims that the prosecutor's cross-examination of his parents, even though he made no specific objection at the time,[9] was so prejudicial to the fairness of the trial that the judge should have disallowed it, and that his failure to do so sua sponte was plain error. We disagree.
Grayton's parents testified on direct examination that he was at their house from about 1:00 a.m. until 4:45 a.m. or later on the night of the fire. The government had information, however, that on two occasions that night the parents had indicated that they were unaware of their son's whereabouts. On cross-examination the prosecutor asked them both whether they had received a phone call during the relevant time period and whether they had gone to Ms. Jenkins' apartment to look for their son. Each parent consistently answered these questions in the negative. The prosecutor then recalled Ms. Jenkins as a rebuttal witness to testify that, both in a phone call after she discovered the fire and again later when the Graytons came to her apartment, they told her that they did not know where their son was.
Ms. Jenkins' account directly contradicted Mr. and Mrs. Grayton's testimony, and the prosecutor had a right to cross-examine them about this contradiction. Contrary to Grayton's argument, the fact that a witness is likely to give negative answers to a series of questions does not preclude an examiner from asking those questions. This method of cross-examination gives the jury an opportunity to determine the credibility of the witness' account by observing the demeanor, facial expressions, and body language of the witness as he or she testifies. The prosecutor's cross-examination of Grayton's parents was relevant, was well within the scope of the direct examination, and was entirely proper. See Elliott, supra, 633 A.2d at 32 (trial judge has discretion to determine scope and extent of cross-examination).

III
We hold that the trial court committed no reversible error. Grayton's convictions are therefore
Affirmed.
NOTES
[1]  D.C.Code § 22-1801(b) (1996).
[2]  D.C.Code § 22-401 (1996).
[3]  D.C.Code § 22-403 (1996).
[4]  D.C.Code § 22-2307 (1996).
[5]  Jenkins testified that Grayton had made the "burning bed" threat many times, whenever he was angry or jealous.
[6]  Ethan King testified that he saw smoke coming from the apartment before Jenkins arrived.
[7]  Detective Webster also testified that the fire was not started by an electrical malfunction, a cigarette, a pipe, or drug usage, and that in his opinion no accelerant or flammable liquid was used. In the unlikely event that an accelerant might have been used on the bedding, "it would have to have been an extreme small amount, such as a capful, maybe."
[8]  The court did say it would allow more specific questions, but defense counsel chose not to proceed further.
[9]  Defense counsel objected to some of the prosecutor's questions but failed to state a basis for his objection.
