Jose Luis Perez (defendant or appellant) appeals from a May 28, 2003 judgment of conviction for conspiracy to distribute cocaine, and the distribution and possession with intent to distribute cocaine, after a jury trial in the United States District Court for the Southern District of New York (Kram, J.). Defendant contends that he is entitled to a new trial because the district court erroneously disqualified a potential juror for cause during the jury impaneling process. He also challenges the trial court’s decision to admit testimony allegedly evincing his consciousness of guilt.
The principal challenge on appeal is to the trial court’s exercise of discretion when it disqualified a prospective juror. Few prospective jurors will admit to bias, and most, when asked if they can be fair and impartial in deciding a matter before them, answer “Yes.” Thus, the law charges the trial judge with ferreting out partiality of a prospective juror during the voir dire. There are no fixed rules of guidance because a variety of disparate factors must be weighed. The trial court, who observes the prospective juror and his demeanor while answering questions, has a superior opportunity to get some sense of the potential juror’s mind-set, and to assess whether that person can decide the case in a truly fair and impartial manner. This exercise by the trial court of its insight, experience, and judgment is one we rarely second guess.
BACKGROUND
Because the legal issues presented for review are not closely related to the specifics of the underlying charges, a brief summary of the facts will suffice.
On October 8, 2002 a grand jury returned a two-count indictment charging Perez with conspiracy to distribute cocaine in violation of 21 U.S.C. § 846, and distribution and possession with intent to distribute five kilograms or more of cocaine in violation of 21 U.S.C. §§ 812, 841(a)(1), and 841(b)(1)(A). The government accused defendant with being involved in a large-scale cocaine distribution business in the Washington Heights section of New York City.
*204The government presented evidence at trial of a several-year investigation into Perez’s drug dealing activities. The evidence introduced included $91,000 in cash seized from his car after a trained dog alerted to the presence of narcotics on the seized money. The prosecution also introduced evidence found in defendant’s apartment after a consensual search, including several firearms and a bulletproof vest. Four cooperating witnesses who had been Perez’s cocaine suppliers or customers testified that he was the man with whom they had conducted drug deals. The last witness, Sugeilis Gutierrez, testified that Perez had paid her to tell a false story to investigators regarding the police stop of Perez in his vehicle that led to the search of his apartment.
Several defense witnesses were presented. Defendant attempted to justify his possession of the substantial amount of cash found in his car by calling witnesses who testified that the seized cash was derived from his grocery store businesses. He also offered character witnesses who spoke to his good reputation in the community, and several residents of his apartment building testified they had never seen any drug dealing in the building. Defendant did not testify.
The jury returned guilty verdicts on both counts of the indictment. On May 14, 2003 the trial court sentenced Perez to 292 months incarceration, five years supervised release, a $35,000 fine, and a $200 special assessment. Defendant filed a timely motion for a verdict of acquittal pursuant to Federal Rule of Criminal Procedure 29(c) or a new trial pursuant to Rule 33, in which he raised the same issues presently before us. The motion was denied and defendant is currently serving his sentence.
Perez’s most substantial point on appeal is that the district court abused its discretion by disqualifying a prospective juror during voir dire, that is, during the preliminary examination of a prospective juror by a judge to decide whether such person is qualified and suitable to serve on the jury. See Black’s Law Dictionary 1569 (7th ed.1999). Defendant contends the disqualification violated his Sixth Amendment right to a fair trial, and that he is therefore entitled to have his conviction vacated and a new trial ordered. Perez’s other challenge is to the district court’s decision to admit the testimony of Ms. Gutierrez, who testified that Perez gave her money to lie to investigators. Perez argues that this testimony had minimal probative value, yet had the potential for substantial prejudice. He maintains this error was not harmless and also entitles him to a new trial. We discuss these two challenges in order.
DISCUSSION
I Disqualification of Juror
A. In General
The Sixth Amendment to the Constitution guarantees a defendant the right to a speedy and public trial by an impartial jury. U.S. Const, amend. VI; see, e.g., United States v. Torres, 128 F.3d 38, 42 (2d Cir.1997). Because “[o]ne touchstone of a fair trial is an impartial trier of fact,” McDonough Power Equip., Inc. v. Greenwood, 464 U.S. 548, 554, 104 S.Ct. 845, 78 L.Ed.2d 663 (1984), the right to an impartial jury also implicates due process rights.
An impartial jury is one “capable and willing to decide the case solely on the evidence before it,” id. at 554, 104 S.Ct. 845, or one comprising people “who will conscientiously apply the law and find the facts,” Wainwright v. Witt, 469 U.S. 412, 423, 105 S.Ct. 844, 83 L.Ed.2d 841 (1985). “Impartiality is not a technical conception. It is a state of mind. For the ascertain*205ment of this mental attitude of appropriate indifference, the Constitution lays down no particular tests and procedure is not chained to any ancient and artificial formula.” United States v. Wood, 299 U.S. 123, 145-46, 57 S.Ct. 177, 81 L.Ed. 78 (1936).
Impaneling a jury requires a trial judge to assess carefully the demeanor and tone of prospective jurors to determine if there is any potential for prejudice. District courts, of necessity, have both broad discretion and a duty to ensure that the jury ultimately impaneled is unbiased. The determination of whether a juror can serve impartially will not be disturbed absent a clear abuse of discretion. See United States v. Garcia, 936 F.2d 648, 653 (2d Cir.1991). In fact, we have stated that “[tjhere are few aspects of a jury trial where we would be less inclined to disturb a trial judge’s exercise of discretion, absent clear abuse, than in ruling on challenges for cause in the empanelling of a jury.” United States v. Ploof, 464 F.2d 116, 118-19 n. 4 (2d Cir.1972).
B. Voir Dire In This Case
In appellant’s case, Judge Kram conducted an extensive voir dire designed to ensure an impartial jury. The process began with the district court judge asking potential jurors a series of general questions relating to their ability to remain impartial. She asked, for example, whether the jurors had any prior knowledge of the case, had any relationship to the defendant or the prosecutors, or otherwise felt they were biased for or against the defendant or the government. In the course of the jury selection, the trial court struck 15 prospective jurors for cause.
Prospective juror Roberto B. English informed the court that he lived on the same city block the government alleged was the site of the defendant’s drug transaction; he had a brother who worked for the federal government in Maryland; and he was himself an attorney. When asked about his legal practice, English responded, “Mainly do insurance litigation, some property subrogation. I do have a background in some criminal defense. I recently completed the federal criminal practice institute.” The trial court went on to ask him several more questions and ultimately inquired whether he felt he could be a fair and impartial juror, to which English responded affirmatively.
The prosecution asked for further voir dire on this potential juror’s criminal defense work. Assistant United States Attorney David Berardinelli was permitted to further interrogate English. The following exchange took place:
Q. Did you indicate that you did any criminal defense work?
A. Yes.
Q. For whom?
A. Well, I’m admitted in New Jersey, and part of admission to New Jersey is pro bono assignments, usually criminal matters. I haven’t gotten an assignment very recently, but occasionally that does come up. Prior to starting with the firm that I’m currently employed with ... I was in private practice where I did some criminal defense work. Mostly — all in the state court level.
Q. Narcotics work?
A. No, no. No felonies. Usually misdemeanors, violations. But no felony work.
Q. I see. And you took a course in federal practice?
A. Yes, at the New York County Lawyers Association — it was about two weeks ago — for a federal criminal trial practice as kind of a precursor *206to admission to the CJA [Criminal Justice Act] Panel.
Q. I see. The CJA panel in this court?
A. Yes.
The prosecution thereafter moved to disqualify English for cause because of a potential for bias. Judge Kram disqualified English over the defense’s objection. In her later ruling denying appellant’s request for a new trial, she explained that English had been “excused for cause after the Court inquired as to the extent of his criminal defense background. The prospective juror had represented pro bono clients in criminal cases in New Jersey state courts and had recently completed a course in federal criminal practice through the New York County Lawyers Association.”
C. Challenges For Cause
In certain circumstances, a court is obliged to dismiss a juror for bias. If, for example, a juror affirmatively stated during voir dire that he was unable to act impartially, or if the juror was a close relative of a party, the juror must be dismissed. See, e.g., United States v. Haynes, 398 F.2d 980, 983-84 (2d Cir. 1968). The categories of mandatory dismissal are few, but they are essential to preserving the objectivity of the jury. Attorney English does not fall into one of the classifications counseling mandatory dismissal. The court did not find actual bias — indeed, English affirmatively stated he could be impartial — and there are no circumstances in the present case compelling a presumption of bias.
Beyond the categories of compulsory dismissal,' district courts retain discretion to dismiss a juror whose voir dire answers evince a sufficient risk of partiality, but not so great that the presumption of bias is mandatory. Torres, 128 F.3d at 46-47. A judge’s discretionary dismissal is upheld when an appellate court is satisfied that the trial judge received responses that permit an inference that the prospective juror would not be able to decide the case before him objectively. The dismissal determination must be grounded in facts developed at voir dire. Id. We must therefore review the district judge’s exercise of discretion based upon the facts elicited during English’s voir dire to decide whether his answers support an inference of bias.
Appellant vigorously insists that the district judge abused her discretion in excusing English. He maintains that nothing in the record supports English’s disqualification and that facts elicited through voir dire were insufficient to infer bias. Perez believes that the trial judge’s decision has the effect of disqualifying an entire occupational group, i.e., the criminal defense bar, from jury service.
Contrary to appellant’s argument, the district court did not excuse the juror simply because he had done criminal defense work, but rather because of the totality of the circumstances, including his ongoing efforts to become a member of the CJA panel for the Southern District of New York. Appellant’s reliance therefore on United States v. Salamone, 800 F.2d 1216 (3d Cir.1986), in which the Third Circuit reversed a district court’s decision to exclude categorically all members of the National Rifle Association without any individualized voir dire, is inapposite. The trial judge engaged English in individualized questioning and did not disqualify him based on any obviously impermissible reason.
Appellant’s arguments highlight the need already noted earlier for deference to a district court when reviewing the voir dire process. Attorney English faced the type of individualized questioning that is *207required to make bias assessments and the court’s finding of bias necessarily depended in large measure on the demeanor and tone of the prospective juror. For example, when asked if he had done any narcotics defense work, Mr. English responded, “No, no. No felonies. Usually misdemeanors, violations. But no felony work.” As written, this is an ambiguous response, since the prospective juror was asked if he did any narcotics work, not merely felony work. However, we are not in a position to know whether the potential juror’s response was vehement, or emphatic, or evasive.
In any event, we need not decide whether the district court abused its discretion because appellant cannot demonstrate a constitutional violation. To succeed on a constitutional challenge based on an error during voir dire, appellant must show that his conviction was at the hands of a biased jury. United States v. Rubin, 37 F.3d 49, 54 (2d Cir.1994); accord United States v. Morales, 185 F.3d 74, 84 (2d Cir.1999); United States v. Towne, 870 F.2d 880, 885 (2d Cir.1989). Perez does not dispute that the jury that convicted him was fair and impartial. Thus, any potential error in the voir dire ruling was harmless.
D. Gray v. Mississippi Distinguished
Perez relies heavily on Gray v. Mississippi, 481 U.S. 648, 107 S.Ct. 2045, 95 L.Ed.2d 622 (1987), to support his argument that exclusion of English from the jury panel was reversible error. In Gray the Supreme Court held the erroneous exclusion of a juror for cause in a capital prosecution was reversible error not subject to harmless error review. That case however involved a jury that convicted petitioner of a capital crime and sentenced him to death, after a prospective juror who had voiced general objections to the death penalty was erroneously stricken. While upholding defendant’s conviction, the Court vacated the sentence of death and remanded for resentencing out of concern for “a capital defendant’s constitutional right not to be sentenced by a ‘tribunal organized to return a verdict of death.’ ” Id. at 668, 107 S.Ct. 2045 (quoting Witherspoon v. Illinois, 391 U.S. 510, 521, 88 S.Ct. 1770, 20 L.Ed.2d 776 (1968)).
Appellant’s attempt to extend Gray beyond the scope of capital sentencing is foreclosed by the Supreme Court’s decision, just one year later, in Ross v. Oklahoma, 487 U.S. 81, 108 S.Ct. 2273, 101 L.Ed.2d 80 (1988). In Ross, the Court stated
We decline to extend the rule of Gray beyond its context: the erroneous “Witherspoon exclusion” of a qualified juror in a capital case. We think the broad language used by the Gray Court is too sweeping to be applied literally, and is best understood in the context of the facts there involved.
Id. at 87-88,108 S.Ct. 2273.
In Ross, the Supreme Court rejected a defendant’s argument that the loss of a peremptory challenge, without more, constitutes a violation of the constitutional right to an impartial jury. The trial court in Ross had erroneously refused to excuse a biased juror for cause, forcing the defendant to use a peremptory challenge. The Court held that so long as the jury that ultimately sits is impartial, the fact that the defendant had to use a peremptory challenge to achieve an unbiased jury does not translate into a Sixth Amendment violation. Id. at 88, 108 S.Ct. 2273; see also United States v. Martinez-Salazar, 528 U.S. 304, 317, 120 S.Ct. 774, 145 L.Ed.2d 792 (2000) (when a defendant elects to use a peremptory challenge to cure an error and is ultimately convicted by an impartial *208jury, there has been no due process violation).
Perez tries to evade the limitation of Gray to capital cases by citing a recent Second Circuit opinion, United States v. Nelson, 277 F.3d 164 (2d Cir.2002), which he believes applied Gray to a non-capital case. Appellant points out that in a footnote, the Nelson court observed that “ ‘among those basic fair trial rights “that can never be treated as harmless” is a defendant’s “right to an impartial adjudicator, be it judge or jury.” ’ ” Id. at 204 n. 48 (quoting Gomez v. United States, 490 U.S. 858, 876, 109 S.Ct. 2237, 104 L.Ed.2d 923 (1989) (quoting Gray v. Mississippi 481 U.S. 648, 668, 107 S.Ct. 2045, 95 L.Ed.2d 622 (1987))). Appellant relies on this dicta for the proposition that jury impaneling errors can never be harmless even in non-capital cases. He is mistaken.
Assuming Nelson can be read to preclude harmless error analysis in the circumstances of that case, the error in Nelson that we held to be “structural” and, therefore, not subject to harmless error review was the erroneous impaneling of a biased juror. Here, however, we are concerned with the erroneous exclusion of an unbiased juror when the jury ultimately impaneled is impartial. Not every error during voir dire compels a new trial, and outside of the limited realm that Gray carved out for capital sentencing, the inquiry we ordinarily engage in asks whether an error of exclusion resulted in prejudice to the defendant. Since appellant does not contest that the jury ultimately impaneled was fair and impartial, his allegation of error does not implicate his constitutional right to a fair trial. See Towne, 870 F.2d at 885 (“Since appellant has in no way established the partiality of the jury that ultimately convicted him, he may not successfully claim deprivation of his sixth amendment or due process rights.”).
II Admission of Consciousness of Guilt Testimony
We turn to the evidentiary challenge. On September 15, 1999 Perez had an encounter with police that resulted in a consensual search of his apartment. During that search, police seized several important pieces of evidence, including multiple firearms and a bulletproof vest. Before trial, defendant sought to exclude the evidence seized from his apartment on the ground that the police had not obtained consent for the search and seizure. The district court held a hearing and denied appellant’s motion to suppress. In its written ruling, the district court relied on the testimony of two police officers, Investigator William Kelly and Detective Juan Checo, who had testified that the search was consensual.
Several weeks after this ruling, Sugeilis Gutierrez told defense investigators she had witnessed the police stop that led to the search, and that, contrary to the officers’ testimony, police had approached appellant on the street with guns drawn, then handcuffed him and forcibly removed his apartment keys from his pocket. An investigator recorded his conversation with Ms. Gutierrez without her knowledge, and this tape was turned over to the United States Attorney’s office. The government interviewed Ms. Gutierrez regarding the contents of the tape, at which point she admitted that her statements on the tape were false and that Perez had paid her to lie to investigators.
Ms. Gutierrez testified at trial that she had met four times with appellant and on each occasion he asked her to give a false statement to investigators regarding the circumstances of the search. She said that Perez had offered her more than $5,000 and a trip to the Dominican Republic in exchange for her making false statements. The court admitted this testimony *209for the limited purpose of showing defendant’s consciousness of guilt, and it gave the jury a limiting instruction to that effect.
Perez argues that since the legality of the search had already been definitively decided by the district court before trial, Ms. Gutierrez’s testimony was not relevant to the issues at trial, namely his alleged participation in a drug conspiracy. Further, he asserts that at most, Ms. Gutierrez admitted she had been asked to lie to appellant’s own investigators, not to give false testimony in court, and that the case law limits the admissibility of consciousness of guilt testimony to circumstances in which a defendant asks a witness to testify falsely. Appellant believes the admission of Ms. Gutierrez’s testimony was unfairly prejudicial and requires a new trial.
As a general matter, all relevant evidence is admissible under the Federal Rules of Evidence unless specifically excluded. See Fed.R.Evid. 402. Relevant evidence is “evidence having any tendency to make the existence of any fact that is of consequence to the determination of the action more probable or less probable than it would be without the evidence.” Fed. R.Evid. 401. District courts have broad discretion to assess the relevancy of evidence and we will not overturn that determination unless it is arbitrary or irrational. United States v. Cruz, 797 F.2d 90, 95 (2d Cir.1986).
Evidence of a party’s consciousness of guilt may be relevant if reasonable inferences can be drawn from it and if the evidence is probative of guilt. See 2 Jack B. Weinstein & Margaret A. Berger, Weinstein’s Federal Evidence, § 401.08 (2d ed.1997). Such evidence is admissible if the court (1) determines that the evidence is offered for a purpose other than to prove the defendant’s bad character or criminal propensity, (2) decides that the evidence is relevant and satisfies Rule 403, and (3) provides an appropriate instruction to the jury as to the limited purposes for which the evidence is introduced, if a limiting instruction is requested. United States v. Mickens, 926 F.2d 1323, 1328-29 (2d Cir.1991).
We have upheld the admission of various kinds of evidence on the ground that it demonstrated consciousness of guilt. For example, proof of defendant’s flight after a charged crime occurred may be admissible even though that evidence might be subject to varying interpretations. See United States v. Ayala, 307 F.2d 574, 576 (2d Cir.1962) (Marshall, J.). Likewise, we have upheld the admission of evidence of attempted witness or jury tampering as probative of a defendant’s consciousness of guilt. See Mickens, 926 F.2d at 1329. While falsehoods told by a defendant in hope of evading prosecution are not themselves sufficient evidence on which to base a conviction, such falsehoods may strengthen an inference of guilt supplied by other evidence. See United States v. Glenn, 312 F.3d 58, 69 (2d Cir.2002); United States v. Johnson, 513 F.2d 819, 824 (2d Cir.1975).
We have no trouble concluding that the district court did not abuse its discretion by permitting Ms. Gutierrez to testify. Appellant’s intent and knowledge were at issue during the trial, and a jury could rationally have found that Ms. Gutierrez’s testimony was probative of appellant’s state of mind. Since other evidence was presented relating to appellant’s knowledge and intent, Ms. Gutierrez’s testimony merely strengthened inferences that were derived from other evidence. The court’s limiting instruction adequately informed the jury of how it could appropriately consider Ms. Gutierrez’s testimony.
As to whether the testimony’s probative value was substantially out*210weighed by the risk of unfair prejudice, see Fed.R.Evid. 403, we review that determination also for abuse of discretion. United States v. Baez, 349 F.3d 90, 94 (2d Cir. 2003) (per curiam). The trial court reasonably concluded that the testimony was probative of appellant’s state of mind, and the court conscientiously weighed that probity against the prejudice the testimony might engender. It determined that since the attempted coercion of the witness was nonviolent, it was no more sensational than the other evidence of the alleged narcotics crimes. Such ruling was not an abuse of discretion.
CONCLUSION
We have considered appellant’s remaining arguments and find them all to be without merit. Accordingly, the judgment of conviction is affirmed.
However, the mandate in this case will be held pending the Supreme Court’s decision in United States v. Booker, — U.S. -, 125 S.Ct. 11, 159 L.Ed.2d 838, No. 04-104, and United States v. Fanfan, — U.S.-, 125 S.Ct. 12, 159 L.Ed.2d 838, No. 04-105. Should any party believe there is a need for the district court to exercise jurisdiction prior to the Supreme Court’s decision, it may file a motion seeking issuance of the mandate in whole or in part. Although any petition for rehearing should be filed in the normal course pursuant to Rule 40 of the Federal Rules of Appellate Procedure, the court will not reconsider those portions of its opinion that address the defendant’s sentence until after the Supreme Court’s decision in Booker and Fanfan. In that regard, the parties will have until 14 days following the Supreme Court’s decision to file supplemental petitions for rehearing in light of Booker and Fanfan.