
584 F.3d 471 (2009)
UNITED STATES of America, Appellee,
v.
John McCALLUM, Jr., also known as John John, also known as C.O. Black, Defendant-Appellant,
Darryl Wright, also known as "D", Defendant.
Docket No. 08-0322-cr.
United States Court of Appeals, Second Circuit.
Argued: December 2, 2008.
Decided: October 19, 2009.
*473 Nola B. Heller, Assistant United States Attorney (Jonathan S. Kolodner, Assistant United States Attorney, on the brief), for Michael J. Garcia, United States Attorney for the Southern District of New York, New York, N.Y., for Appellee.
Joseph A. Vita, Law Office of Joseph A. Vita, Esq., Port Chester, N.Y., for Appellant.
Before: JACOBS, Chief Judge, McLAUGHLIN and B.D. PARKER, Circuit Judges.
B.D. PARKER, JR., Circuit Judge:
Defendant-Appellant John McCallum Jr. appeals from a judgment of conviction in the United States District Court for the Southern District of New York (Robinson, J.). McCallum was convicted of various narcotics offenses involving crack cocaine and was sentenced principally to 240 months' incarceration. We write to address McCallum's primary contention, which is that the District Court abused its discretion in admitting as similar acts evidence two of his prior narcotics convictions. We conclude that the admission of this evidence, while an abuse of discretion, was harmless error. In a related but separately filed summary order, we dispose of McCallum's other claims of trial error.

BACKGROUND
At trial, the government proved that McCallum and his co-conspirators operated a substantial crack cocaine distribution business in and around Spring Valley, New York. The conspiracy and substantive offenses charged in the indictment involved narcotics activities that occurred between approximately September of 2004 and May of 2005, and that culminated in four controlled buys of narcotics in April and May of 2005. After the final controlled buy, police officers executed a search warrant at McCallum's residence and recovered substantial quantities of drugs.
At trial, the government proved McCallum's involvement in the conspiracy through the testimony of co-conspirator and cooperating witness Darryl Wright, who was McCallum's partner and resided in the same apartment as McCallum. The government also offered the testimony of Lenell Brookins, a roommate of McCallum and Wright, and the testimony of police officers who had observed McCallum engaging in narcotics transactions and had searched the apartment where the narcotics were seized. The government's other evidence included audio recordings in which a confidential informant, David DeFreese, purchased crack cocaine from Wright and McCallum, and phone records indicating narcotics transactions.
Prior to trial, the government informed the court that it intended to introduce evidence of McCallum's two prior narcotics felony convictions for possession and attempted sale of cocaine. Although the government had at hand the drugs that had been seized, the testimony of McCallum's partner about their extensive drug-dealing, and a plethora of other evidence of prior narcotics activities, the government nevertheless argued that evidence of the 2003 convictions was critical to prove that McCallum knew that the substances he sold were narcotics and that he intended to sell them. The government also asserted that it wished to introduce the periods of incarceration McCallum had served on the two convictions because, without them, "much of the charged conspiracy will be difficult for the jury to understand." The court agreed, without significant discussion, *474 to receive the convictions but not evidence of the periods of incarceration. The record sheds little light on why the court believed the convictions were admissible.
During voir dire, potential jurors were asked whether they would be able to follow instructions requiring them to consider the convictions only for the limited purpose of evaluating the defendant's knowledge and intent, and whether, after learning of the convictions, they would be able to maintain their presumption of the defendant's innocence. Over the defense's objections, the District Court received evidence of the convictions in the form of a stipulation during the government's case in chief.[1] During the court's final charge, the jury was given a limiting instruction with respect to the convictions.[2] At the conclusion of the trial, McCallum was convicted of three of the four counts in the indictment, including conspiracy and two substantive narcotics offenses. This appeal followed.

DISCUSSION
We review a district court's admission of evidence of prior crimes for abuse of discretion. See United States v. Lombardozzi, 491 F.3d 61, 78-79 (2d Cir.2007). Abuse of discretion occurs when the court acts in "an arbitrary and irrational manner." Id. A district court's decision to admit evidence is subject to harmless error analysis. Fed.R.Crim.P. 52(a); United States v. Madori, 419 F.3d 159, 168 (2d Cir.2005). The main harmless error inquiry is whether the contested testimony was unimportant in relation to everything else the jury considered on the issue in question, as revealed in the record. See United States v. Garcia, 413 F.3d 201, 217 (2d Cir.2005) (holding that erroneous admission of evidence was harmless where it "had no substantial and injurious effect or influence on the jury verdict" (internal quotation marks omitted)).
Evidence of prior convictions may be admissible under Federal Rule of Evidence 404(b) to show "intent, ... knowledge, *475 identity, or absence of mistake or accident," but not to show character or propensity. Fed.R.Evid. 404(b). Where prior convictions are concerned, the line between intent or knowledge and character or propensity is often a fine one, requiring the thoughtful, focused attention of the district court. The most important reason why this attention is required is that the introduction of prior convictions, unless carefully handled, will undermine the presumption of innocence.
When reviewing the admission of evidence pursuant to Rule 404(b), we consider whether (1) the prior crimes evidence was "offered for a proper purpose;" (2) the evidence was relevant to a disputed issue; (3) the probative value of the evidence was substantially outweighed by its potential for unfair prejudice pursuant to Rule 403; and (4) the court administered an appropriate limiting instruction. Huddleston v. United States, 485 U.S. 681, 691-92, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988). Our Circuit takes an inclusionary approach to the admission of prior crimes evidence, under which such evidence "is admissible for any purpose other than to show the defendant's criminal propensity." United States v. Paulino, 445 F.3d 211, 221 (2d Cir.2006) (citing United States v. Pitre, 960 F.2d 1112, 1118-19 (2d Cir.1992)). Yet this inclusionary approach does not invite the government "to offer, carte blanche, any prior act of the defendant in the same category of crime." United States v. Garcia, 291 F.3d 127, 137 (2d Cir.2002); see also id. at 138 (holding that prior conviction for selling cocaine should not have been admitted to prove intent and knowledge of the charged sale of cocaine, because "the government offered and the court admitted the prior conviction as relevant for a very specific purposeto show that [defendant] knew that [a] taped phone conversation was about a coded drug transactionbut made no attempt to link the transaction on that basis").
Where such evidence is offered for the purpose of establishing the defendant's knowledge or intent, we require that the government "identify a similarity or connection between the two acts that makes the prior act relevant to establishing knowledge of the current act." Id. at 137; see also id. at 138 (holding that admission of prior conviction was abuse of discretion because "the government did not establish that [the] prior drug conviction was meaningfully probative of [the defendant's] knowledge" with respect to the charged narcotics conspiracy; "[t]he only similarity between the two drug transactions ... [was] that both involved cocaine"; and "[t]he government did not offer evidence of any other similarity or connection between the two transactions"); United States v. Brand, 467 F.3d 179, 197 (2d Cir.2006) (government must show "similarity or some connection" of prior act evidence to charged crime in order to establish that the prior act is relevant to a disputed element, such as intent (internal quotation marks omitted)); United States v. LaFlam, 369 F.3d 153, 156 n. 1 (2d Cir.2004) (per curiam) (same).
Although the record is not entirely clear, the government offered McCallum's prior convictions ostensibly to establish McCallum's intent to deal drugs and his knowledge of drug dealing. In any event, as the government correctly contends, McCallum did not concede those issues. In a pretrial memorandum addressing the point, counsel stated: "As McCallum's counsel I cannot say at this point unequivocally whether or not knowledge and or intent will be disputed issues in this case." Because McCallum's counsel did not make a statement to the court of sufficient clarity to indicate that intent and knowledge would not be disputed, those issues remained *476 sufficiently in dispute for the similar acts evidence to be relevant and hence admissible. See United States v. Colon, 880 F.2d 650, 659 (2d Cir.1989). Under these circumstances, the evidence was admissible during the government's case in chief. See United States v. Inserra, 34 F.3d 83, 89-90 (2d Cir.1994); United States v. Zackson, 12 F.3d 1178, 1182-83 (2d Cir.1993).
Once the first two prongs of Huddleston are satisfied, the court is then required to consider the third prong and decide whether the probative value of the prior crimes is substantially outweighed by the danger of unfair prejudice. In Old Chief v. United States, 519 U.S. 172, 117 S.Ct. 644, 136 L.Ed.2d 574 (1997), the Supreme Court defined "unfair prejudice" as "an undue tendency to suggest decision on an improper basis," id. at 180, 117 S.Ct. 644 (internal quotation marks omitted), and invoked as an example a jury's "generalizing a defendant's earlier bad act into bad character and taking that as raising the odds that he did the later bad act now charged (or, worse, as calling for preventive conviction even if he should happen to be innocent momentarily)," id. at 180-81, 117 S.Ct. 644. In this regard, evidence of prior convictions merits particularly searching, conscientious scrutiny. Such evidence easily lends itself to generalized reasoning about a defendant's criminal propensity and thereby undermines the presumption of innocence. Despite the most careful instructions from the court, the risk is present that jurors are likely to believe that if a defendant previously was convicted of drug offenses, there is a high probability that he is guilty of the drug offense for which he is on trial. See 1A Wigmore, Evidence § 58.2 (Tillers rev. 1983) (stating that, where prior crimes evidence is adduced, "[t]he natural and inevitable tendency of the tribunal ... is to give excessive weight to the vicious record of crime thus exhibited and either to allow it to bear too strongly on the present charge or to take the proof of it as justifying a condemnation, irrespective of the accused's guilt of the present charge"). Moreover, prior convictions are far more likely to be received as potent evidence of propensity than other prior bad acts routinely offered under Rule 404(b) because they bear the imprimatur of the judicial system and indicia of official reliability. See 1 Mueller & Kirkpatrick, Federal Evidence § 4:30 (3d ed. 2007) ("In the common situation in which a prior crime is proved by means of a conviction, this very fact brings home to a jury that another jury considered the defendant guilty and blameworthy, which in that sense magnifies the underlying deed.").
Consequently, as we have repeatedly held, prior convictions should not be admitted unless the court has carefully conducted the Rule 403 balancing test required by Huddleston. See, e.g., United States v. Salameh, 152 F.3d 88, 110 (2d Cir.1998) (per curiam) ("To avoid acting arbitrarily, the district court must make a `conscientious assessment' of whether unfair prejudice substantially outweighs probative value." (quoting United States v. Birney, 686 F.2d 102, 106 (2d Cir.1982))); United States v. Williams, 596 F.2d 44, 51 (2d Cir.1979) ("District judges must carefully scrutinize both the basis for the claimed relevance of [prior crimes] evidence and the balance between its probative value and prejudicial effect. The key to a fair trial in such cases is careful determination by the trial judge of both issues, particularly the latter." (emphases added)).
There is no indication in the record that the District Court engaged at all in the Rule 403 inquiry, let alone the required conscientious one. In ruling on the *477 government's pre-trial Rule 404(b) motion, the court stated:
I will allow the government to admit information of Mr. McCallum's two felony drug convictions in 2003. Again, it is relevant under 404(b) showing intent, knowledge and motive. It is relevant under 609 if we were to look at it as a cross-examination issue. But I'm ruling that the government will be able to offer that information in their case in chief.
The court's sole reference to prejudice occurred after it had decided to admit the convictions, and even then, the court expressed concern only over the prejudicial impact of proof of McCallum's periods of incarceration. At that point, defense counsel renewed its objection to the admission of the evidence and stated, "I would certainly ask that your Honor not permit any proof of the sentence received [for the 2003 convictions].... I believe that factor may be a prejudicial one." To this, the court replied, "You know what? I'm going to agree with that," and the government agreed to redact the proof of incarceration from the stipulation.
Because the court gave no explanation for its conclusion that the prior convictions evidence should be admitted, we are significantly constrained in our review of the court's application of the unfair prejudice prong of Huddleston. Without the benefit of its reasoning we are in no position to assume that the court appreciated the seriousness of the risk that introducing the convictions would undermine the fairness of the trial. McCallum's two prior convictions for the same type of conduct for which he was on trial appears to us to be classic, and powerful, evidence of propensity.
The convictions were offered for the ostensible purpose of proving knowledge and intent. Even though these issues were not conceded, we are unable to discern from the record why the District Court thought the issues were seriously in dispute or why the prior convictions were appropriate proof. See 2 Weinstein, Federal Evidence § 403.02 (Joseph M. McLaughlin, Ed., Matthew Bender & Co. 2009) (stating that a trial judge applying the Rule 403 balancing test to certain evidence "must reject any method that treats each item of evidence `as an island,'" and must instead "evaluate all the pieces of evidence going to the same point," thereby "compari[ng]... evidentiary alternatives"). The government had available for presentation to the jury extensive testimony from McCallum's co-conspirator about the operation of the charged conspiracy and their drug dealings spanning many months. The government also had available drugs that had been seized as well as the results of audio and visual surveillance. Given all of this evidence, we are at a loss to understand how the court or the government could believe that the prior convictions were necessary to prove McCallum's intent and knowledge and that they passed muster under Rule 403. See id. § 404.21 ("[T]he availability of other, less prejudicial, evidence on the same point ordinarily reduces the probative value of a given item of extrinsic evidence.... If the incremental value is slight, and the possibility of prejudice through misuse by the jury great, the court should exclude the evidence under Rule 403."). Our review of the record thus leads us to conclude that the District Court received the convictions as propensity evidence in sheep's clothing and did so with insufficient regard for the unfair prejudice that surely would result from their admission. See United States v. Bell, 516 F.3d 432, 447 (6th Cir.2008). We therefore conclude that the court abused its discretion in admitting the convictions.
We next must determine whether this error was harmless. As we stated *478 in United States v. Al-Moayad, "[a] district court's erroneous admission of evidence is harmless if the appellate court can conclude with fair assurance that the evidence did not substantially influence the jury." 545 F.3d 139, 164 (2d Cir.2008) (internal quotation marks omitted). In reviewing for harmless error, "we principally consider: (1) the overall strength of the prosecution's case; (2) the prosecutor's conduct with respect to the improperly admitted evidence; (3) the importance of the wrongly admitted [evidence]; and (4) whether such evidence was cumulative of other properly admitted evidence." United States v. Kaplan, 490 F.3d 110, 123 (2d Cir.2007) (internal quotation marks omitted). We have repeatedly held that the strength of the government's case is the most critical factor in assessing whether error was harmless. See, e.g., United States v. Lombardozzi, 491 F.3d 61, 76 (2d Cir.2007).
The government's case against McCallum was indisputably strong. Both Wright and Brookins provided detailed testimony about McCallum's role in, and knowledge of, the charged conspiracy. The police officers' eyewitness testimony and the audio recordings confirming McCallum's presence at the controlled buys also were compelling evidence of guilt. Finally, the government introduced physical evidence including substantial quantities of narcotics seized from the apartment and found inside McCallum's boot. This evidence certainly would allow a reasonable juror to conclude that McCallum had dealt drugs. We also note that the government did not draw undue attention to the prior convictions, omitting as it did any discussion of the convictions in its summation or rebuttal. In light of these considerations, and the fact that the prior convictions were cumulative of other admissible evidence bearing on McCallum's knowledge and intent, we conclude that the District Court's admission of the convictions was harmless error.
In a different case, in which prior convictions were admitted but the government's other evidence was not overwhelming, or where the other harmless error factors tilted more strongly in the defendant's favor, or where the government's summation emphasized the prior convictions, a different result could well be indicated. It bears repeating that prior convictions present a singular risk of serious prejudice and that their introduction can jeopardize the fairness of a trial. Typically, their potency in this regard does not depend on testimony or argument by the prosecutors; standing alone, prior convictions are capable of undermining the presumption of innocence and distracting the jury from the business of determining guilt or innocence based on proof of the charges in the indictment. If the decision is made to admit such evidence, the court must provide appropriate limiting instructions and must explain its decision sufficiently to permit appellate review.

CONCLUSION
The judgment of the District Court is affirmed.
NOTES
[1]  The stipulation stated:

On April 9, 2003, John McCallum, Jr., the defendant, was convicted after pleading guilty to criminal possession in the third degree of a controlled substance, namely, cocaine, which is a Class B felony. This crime was committed on March 14, 2002. On April 9, 2003, John McCallum, Jr., was convicted after pleading guilty to attempted criminal sale in the second degree of a controlled substance, namely, cocaine, which is a Class C felony. This crime was committed on December 3, 2002.
[2]  The portion of the jury charge relating to the prior convictions evidence was as follows:

[A] stipulation was read that indicated that the defendant had been convicted in 2003 of two different offenses relating to his possession and sale of cocaine.... The Government offered this evidence to demonstrate the defendant's intent and knowledge, and to establish the absence of mistake or accident with regard to the offenses charged in the instant indictment. You may not consider this evidence as a substitute for proof that the defendant committed any of the crimes charged in the indictment. Nor may you consider this proof as evidence that the defendant has a criminal personality or a bad character. This evidence about the defendant's prior convictions was admitted for a much more limited purpose and you may only consider it for that limited purpose.
Specifically, if you determine that the defendant committed any of the acts charged in the indictment, then you may, but you need not, draw an inference, from the evidence of the defendant's prior convictions, that the defendant acted knowingly and intentionally with respect to the specific charge as charged in the indictment, and not because of some mistake, accident, or innocent other reason. The evidence of the defendant's prior convictions may be considered by you only for the purpose that I have just explained to you.
