Defendant-Appellee Quadri Garnes was charged in the United States District Court for the Eastern District of New York with threatening to assault and murder employees of the United States Postal Service (“USPS”) and transmitting in interstate commerce communications containing one or more threats to injure the person of another, in violation of 18 U.S.C. §§115(a)(1)(B) and (b)(4) and 875(c). The charges arose from a phone call that Garnes made to the New York State Department of Labor (“DOL”). Prior to trial, Garnes moved to exclude five statements that he made during that call, which reference his criminal record. The district court (Morrison, J.) granted his motion and excluded the five statements under Rule 403 of the Federal Rules of Evidence. On appeal, the government argues that the district court exceeded its discretion in excluding the five statements. We agree. The district court incorrectly concluded that the five statements were of “limited” probative value that was outweighed by a danger of unfair prejudice. The statements at issue are in fact highly probative, as they are both a significant part of the threat that is the actus reus of the crime and substantially probative of the required mens rea, the defendant’s intent that his words be understood by the victims as a true threat. Accordingly, we REVERSE the district court’s order of exclusion, and REMAND the case for further proceedings. GERARD LYNCH, C.J. On September 29, 2022, Defendant-Appellee Quadri Garnes called the New York State Department of Labor (“DOL”) to inquire about his eligibility for unemployment benefits based on his brief employment with the United States Postal Service (“USPS”). After being informed that he was ineligible for benefits, Garnes made statements over the phone to two DOL employees that the government alleges constituted true threats to harm USPS officials and others. The alleged threats incorporated five statements that referenced (and indeed overstated) Garnes’s prior criminal record. A grand jury in the Eastern District of New York indicted Garnes on two counts in connection with the September 29, 2022 phone call: threatening to assault and murder employees of the USPS, in violation of 18 U.S.C. §115(a)(1)(B) and (b)(4) (Count One), and transmitting in interstate commerce communications containing one or more threats to injure the person of another, in violation of 18 U.S.C. §875(c) (Count Two). Prior to trial, Garnes moved to require the government to redact the threatening conversation to exclude the five references that Garnes himself made to his criminal history and prior incarceration, citing Rules 401, 402, and 403 of the Federal Rules of Evidence. The government opposed the motion. On July 7, 2023, the district court (Nina R. Morrison, J.) granted Garnes’s motion and excluded the five statements, concluding that the probative value of that evidence is substantially outweighed by a danger of unfair prejudice, confusing the issues, and misleading the jury. On appeal from that order, the government argues that the district court exceeded its discretion in excluding the five statements, because (1) it underestimated their probative value and misapplied Rule 404(b) of the Federal Rules of Evidence and Second Circuit case law to its analysis of unfair prejudice; (2) it did not properly consider the utility of a limiting instruction; and (3) it wrongly relied on the existence of what it considered to be “strong” alternative evidence. For the reasons set forth below, we hold that, in a prosecution for making threats, the district court exceeded its discretion in excluding portions of the threats themselves under Rule 403 of the Federal Rules of Evidence, where those statements, made by the defendant himself, are highly probative, and any unfair prejudice can be substantially reduced by a limiting instruction. Accordingly, we REVERSE the district court’s order of exclusion, and REMAND the case for further proceedings. BACKGROUND I. Factual Background1 Garnes worked as a mail carrier for the USPS from late March or early April 2022 to late May 2022. Following his termination from that position, he applied for unemployment benefits. His claim was denied because he had not worked for the USPS long enough to be eligible for the benefits. On September 29, 2022, Garnes telephoned the DOL to inquire about his unemployment benefit claim. Over the course of a 45-minute phone conversation, Garnes spoke with two DOL employees, who each advised him that he did not qualify for unemployment benefits. In response, Garnes made a series of statements expressing his frustration with that outcome. Some of the statements indicated that Garnes would shoot individuals at the USPS and DOL: “If I go back to the post office, I’m gonna shoot somebody.” Gov’t App’x 81. “Oh, so I gotta go to the post office and shoot the post office up, right?” Id. at 89. “Somebody might get shot today coming out of Department of Labor.” Id. at 90. Other statements conveyed that Garnes’s reaction to the denial of benefits would land him in jail or prison (“Y’all gonna make me go to jail,” id. at 82) and that he was comfortable with that possibility (“I’m made, as long as I’m in the New York City jail, I’m good,” id. at 88). Garnes also acknowledged that he knew the conversation was being recorded: “And I’m putting it out there on, cause I know this is recorded, because if I was to do something like that, at least when they start going through the records, they know why it was done.” Id. at 88. Of particular relevance to this appeal, some of the statements indicated that Garnes had a criminal history, for example: “Cause listen didn’t I just tell you I got 18 and a half years in jail. It don’t bother me to be in jail.” Id. The DOL reported the conversation to the New York State Police and the United States Postal Inspection Service. Law enforcement searched for Garnes and took steps to protect the employees of the DOL and USPS. The DOL also informed its employees of the threats and took additional safety measures. Garnes was arrested two weeks later. II. Procedural History In a superseding indictment dated June 16, 2023, Garnes was charged with threatening to assault and murder officials whose killing would be a crime under 18 U.S.C. §1114, in this instance, employees of the USPS, in violation of 18 U.S.C. §115(a)(1)(B) and (b)(4) (Count One), and transmitting in interstate commerce communications containing one or more threats to injure the person of another, encompassing the DOL employees, in violation of 18 U.S.C. §875(c) (Count Two). On June 23, 2023, Garnes moved in limine to exclude evidence relating to his prior criminal history, namely, the five statements that he made during the phone call with the DOL that referenced his time in jail, his prior felony convictions, and the places of his past incarceration. The five statements that Garnes sought to exclude are: I got 18 and a half years in jail. I got 18 and a half years. No, listen, listen, I have eight. [T]o make myself not stop from robbing a bank. They’re 18 and a half years in jail. [L]ook, look, I got mad felonies. I got like nine, 10 felonies, right? Cause listen didn’t I just tell you I got 18 and a half years in jail. It don’t bother me to be in jail. And I told you I got 18 and [a] half years all together in jail, all together in prison. [N]ot Rikers Island, state prison, state prison, Clinton, A[t]tica, Elm[i]ra state prison. [M]aybe where your, where, where, where, where your place is in Albany. Gov’t App’x 46-47, 81-89.2 Garnes contended that those statements did not constitute threats or statements of intent, but rather, were, “at worst, poorly phrased attempts…to characterize the absurdity of his predicament; one where it is preferable, from an economic standpoint, to be incarcerated than to live as a free man.” Id. at 50. Accordingly, Garnes argued that the five statements should be excluded under Rule 402 of the Federal Rules of Evidence because they are “irrelevant to the charged offense” and, even if they are minimally relevant, under Rule 403 of the Federal Rules of Evidence because they are “highly prejudicial.” Id. at 47. Garnes further argued that the statements are misleading because he had “unintentionally misstate[d]” his criminal history “ in a manner that suggests that it is worse than it actually is,” and that this also increases the danger of unfair prejudice. Id. at 48-49. Although Garnes told the DOL that he had spent 18 and a half years incarcerated in various state facilities as a result of nine or ten felony convictions, in reality, Garnes had been incarcerated for a total of only seven years, in a single institution — Ulster Correctional Facility. The 18-and-a-half-year figure referred to the span of time that Garnes had spent in and out of the criminal justice system, and the reference to nine felonies reflected the number of felonies Garnes had been charged with, though he was convicted of only three. The government opposed Garnes’s motion to exclude, arguing that the five statements are more probative than prejudicial, and are directly probative of the charged offenses. In particular, the government argued that the statements are highly relevant evidence to its required showing of mens rea, because in a true threat prosecution, the government must prove that the defendant had some subjective understanding of the threatening nature of his statements. See Counterman v. Colorado, 600 U.S. 66, 69 (2023). Therefore, the government asserted that the statements should be admitted into evidence with the rest of the recorded phone call. After the final pretrial conference, the district court issued an electronic docket order on July 7, 2023 that granted Garnes’s motion in limine to exclude the five statements, concluding that their probative value is substantially outweighed by a danger of unfair prejudice, confusing the issues, and misleading the jury under Rule 403. The district court also stated that it would provide its reasons for the ruling on the record prior to the beginning of jury selection. Two days later, the government submitted a letter to the district court arguing that, by excluding portions of the September 29, 2022 call, the July 7, 2023 order excluded portions of the charged conduct, which should be admitted because that evidence is highly probative of both the actus reus and the mens rea of the charged offenses. As theorized by the government, that evidence “would allow a jury to assess the criminal conduct in its entirety” and to “reasonably infer” that Garnes repeatedly referenced his criminal history to demonstrate to his victims that his threats should be believed because he had committed crimes in the past and was comfortable with the prospect of returning to jail, which goes to his knowledge and intent. Gov’t App’x 113. The government urged the district court to issue a limiting instruction to address its concerns about undue prejudice, rather than taking the “unprecedented step of excluding, in a trial for threats, portions of the threats themselves.” Id. It proposed a limiting instruction that would explain that the five statements should not be considered for their truth or that Garnes’s account of his criminal history is inaccurate and should not be relied upon for its truth. The district court issued an oral ruling on July 10, 2023 and a memorandum and order on July 12, 2023, adhering to its decision to exclude the five statements and denying the government’s request for a limiting instruction. The court concluded at the threshold that the statements are relevant evidence under Rule 401, particularly as to the question of whether Garnes had the requisite mens rea for his statements to constitute true threats under the two statutes he is charged with violating. Despite the relevance of these statements, the district court excluded them under Rule 403. In conducting the balancing analysis required by that Rule, the court concluded that the probative value of the statements is “limited.” United States v. Garnes, No. 1:22-CR-00487 (NRM), 2023 WL 4489983, at *5 (E.D.N.Y. July 12, 2023). The court compared what it considered to be the available evidentiary alternatives, concluding that Garnes’s explicit statements about shooting and killing people at the DOL and USPS are “much more probative” than Garnes’s statements about his criminal history, and would be available to the government at trial to prove the elements of the crimes charged. Id. at *6. Weighed against that assertedly limited probative value, the court concluded that the statements carry a high risk of unfair prejudice, confusing the issues, and misleading the jury. The court stated that reference to a defendant’s criminal record is always highly prejudicial, and the risk of unfair prejudice in the present case is even higher because the statements at issue inflate Garnes’s criminal record and suggest that he has served more time, in more state facilities, for more felony convictions, than was actually the case. Further, the court concluded that the proposed limiting instruction could not address its concerns regarding the risk of unfair prejudice, confusing the issues, and misleading the jury — it would only “raise more questions than it answers” for the jury. Id. at *7. Accordingly, the court excluded the statements, on the basis that their “limited” probative value is substantially outweighed by a danger of unfair prejudice, confusing the issues, and misleading the jury. Id. at *5. The court went on to recognize that there may be other true threat cases where the government could succeed in admitting statements referencing prior crimes, such as: where it does not also have the benefit of numerous statements evidencing the alleged threats that are separate and apart from references to a defendant’s prior criminal convictions; where the allegedly threatening statements are far less explicit or readily comprehended by a jury than those made here, thus requiring the statements to be contextualized by the defendant’s criminal history; or in which a [d]efendant’s references to his prior record are truly “inextricable” from the [g]overnment’s other proof. Id. at *7. It concluded this was not such a case. This interlocutory appeal followed. DISCUSSION On appeal, the government argues that, in a prosecution for making threatening statements, the district court erred in excluding portions of the threats themselves on the basis that the defendant’s own exaggerated references to his criminal history were unfairly prejudicial under Rule 403 of the Federal Rules of Evidence. We agree. Rule 403 provides that a district court “may exclude relevant evidence if its probative value is substantially outweighed by a danger of,” among other things, “unfair prejudice, confusing the issues, [or] misleading the jury.” Fed. R. Evid. 403. In making a Rule 403 determination, “[a] court should consider the possible effectiveness of a jury instruction and the availability of other means of proof.” United States v. Dupree, 706 F.3d 131, 138 (2d Cir. 2013), citing Fed. R. Evid. 403 advisory committee’s note; see also Fed. R. Evid. 403 advisory committee’s note (“The availability of other means of proof may…be an appropriate factor.”). We grant considerable deference to a district court’s determination to exclude relevant evidence under this rule, recognizing that Rule 403 calls for “on-the-spot balancing,” Sprint/United Mgmt. Co. v. Mendelsohn, 552 U.S. 379, 384 (2008), which district courts are well-positioned to carry out due to their proximity to the detailed circumstances of the case. Accordingly, we will reverse a district court’s ruling on admissibility under Rule 403 as an abuse of discretion only if its conclusion is “arbitrary or irrational.” United States v. Awadallah, 436 F.3d 125, 131 (2d Cir. 2006). As explained below, we hold that the district court erred in excluding the evidence. This case differs from the typical case in which the government seeks to introduce independent evidence of a defendant’s criminal conviction(s), or background conversations or events that allude to a defendant’s time in prison or guilt. See, e.g., United States v. Jamil, 707 F.2d 638 (2d Cir. 1983) (reversing the district court’s exclusion of a tape recording “made by a government informant of a conversation with [the] defendant” that “suggest[ed] that law enforcement officers were interested in the defendant” under Rule 403). By contrast, the statements at issue here were part of the actus reus of the crime. The statements were injected into the case by Garnes himself, as part of the very same conversations in which he made the threats. Their probative value was particularly strong, because a reasonable jury could find that they were powerful indications that Garnes’s statements about shooting USPS and DOL personnel were, and were intended to be, true threats. The jury could find from those statements that Garnes emphasized, and indeed exaggerated, his character as a dangerous person in order to frighten those threatened by suggesting that he had the capacity to carry out his threats, and that he would not be deterred from carrying them out by the threat of punishment. Thus, the inference that Garnes was a violent person was not an unfair inference that one party sought to create in the minds of the jury about its adversary, but an impression that Garnes himself could be found to have sought to create in the minds of the victims. The court also overweighted the prejudicial effect of the statements by failing to recognize the likelihood that the danger of unfair prejudice could be mitigated by a limiting instruction. I. Relevance Because Rule 403 concerns the admissibility of relevant evidence, a district court must first determine, before undertaking the balancing analysis required by Rule 403, whether the evidence at issue is “relevant,” as defined by Rule 401. Relevance describes the relationship between “an item of evidence and a matter properly provable in the case.” Fed. R. Evid. 401 advisory committee’s note. Here, the district court agreed with the government that the five statements that Garnes seeks to exclude are relevant evidence. Nevertheless, to inform the Rule 403 balancing analysis, it is worth elaborating why the evidence is relevant. We begin by explaining the elements of the crimes for which Garnes was to be tried. Garnes was charged with violating 18 U.S.C. §§115(a)(1)(B) and 875(c). Section 115(a)(1)(B) makes it a federal crime to “threaten[] to assault…or murder…an official whose killing would be a crime” under 18 U.S.C. §1114; such officials include USPS employees. The statute also includes an explicit mens rea element: the perpetrator must have made the threats “with intent to impede, intimidate, or interfere with such official…while engaged in the performance of official duties, or with intent to retaliate against such official…on account of the performance of official duties.” 18 U.S.C. §115(a)(1)(B). By contrast, §875(c), which prohibits transmitting in interstate commerce a communication containing any threat to injure another person, does not contain an explicit mens rea element. Elonis v. United States, 575 U.S. 723, 734 (2015) (“The most we can conclude from the language of Section 875(c) and its neighboring provisions is that Congress meant to proscribe a broad class of threats in Section 875(c), but did not identify what mental state, if any, a defendant must have to be convicted.”). In Elonis, however, the Supreme Court determined that §875(c) “requires that the defendant be aware of the threatening nature of [his] communication,” id. at 726, drawing on the “universal and persistent” principle that “wrongdoing must be conscious to be criminal,” id. at 734, quoting Morissette v. United States, 342 U.S. 246, 250, 252 (1952). Because it is not a criminal act to transmit communications in interstate commerce, “the mental state requirement must…apply to the fact that the communication contains a threat.” Id. at 737. The Court therefore held that a defendant convicted under §875(c) must have some awareness of the risk that the communication will be viewed as a threat — a negligence standard would not accord with the principle that criminal defendants must be conscious of their wrongdoing to be convicted. See id. at 737-39. But the Court left open the question of the minimum mental state required for criminal conviction under §875(c). See id. at 741-42. During the pendency of this case, the Supreme Court answered a related but broader question by addressing the constitutionally required elements of all criminal prohibitions of threatening statements. See Counterman, 600 U.S. 66. The Court concluded that the need to protect the freedom of speech guaranteed by the First Amendment affects both the act and intent elements of threat crimes. With respect to the prohibited act, the Supreme Court acknowledged that “true threats” constitute a category of communication that falls outside of the protective scope of the First Amendment. Id. at 74, citing Virginia v. Black, 538 U.S. 343, 359 (2003). Historically, it has been thought that proscribing true threats of violence prevents “fear of violence and the disruption that fear engenders.” Black, 538 U.S. at 344. But the First Amendment protects even intemperate speech, and words that take a threatening form may simply reflect heated rhetoric that, in context, would not reasonably engender fear. Thus, to be consistent with the First Amendment, a threat crime requires an objective element (the actus reus) — the threatening words must constitute a true threat. See Counterman, 600 U.S. at 74 (“The ‘true’ in that term distinguishes what is at issue from jests, ‘hyperbole,’ or other statements that when taken in context do not convey a real possibility that violence will follow….”). The existence of a true threat depends on what the statement conveys to the person to whom it is directed, rather than on the mental state of the speaker. Id. (citing Elonis, 575 U.S. at 733). But the First Amendment also “demand[s] a subjective mental-state requirement.” Id. at 75. Such a mens rea element may ultimately shield some true threats from liability because “it makes prosecution of otherwise proscribable, and often dangerous, communications harder,” but is necessary to ensure that protected speech will not be “chill[ed]” by fear of unwarranted prosecution. Id. at 78. The Court determined that the minimum mens rea element required by the First Amendment in threat cases is recklessness. Id. at 78-79. “ In the threats context, [recklessness] means that a speaker is aware that others could regard his statements as threatening and delivers them anyway.” Id. at 79 (internal quotation marks omitted). Accordingly, to succeed in prosecuting Garnes under the two statutes, the government must show both that the statements he made would, objectively, convey to the listener that the threatening language represented a genuine threat, and that in making his statements, he “consciously disregarded a substantial risk that his communications would be viewed as threatening violence” to the USPS and DOL employees. Id. at 69. Moreover, in the case of 18 U.S.C. §115(a)(1)(B), the statute requires an additional, even more demanding mental element — the intent to impede, intimidate, interfere with, or retaliate against USPS officials. These are meaningful requirements. Even where a defendant’s words are literally threatening, it will remain open to a defendant to attempt to raise a reasonable doubt in the minds of jurors about whether those statements would be taken as genuine threats by those “threatened,” and about whether the speaker intended, or at least was conscious of the risk, that they would be so taken.3 In assessing whether those elements have been proven beyond a reasonable doubt, context matters. The literal, threatening words may take on greater or lesser seriousness from the additional statements that surround them. Accordingly, the five statements made by Garnes that repeatedly refer to, and indeed overstate, his criminal history, at a minimum have a “tendency” to make it more probable that the threatening language would convey to listeners that they had something to fear, and that Garnes made those statements with an awareness, and even with the intention, that he would create such fear. See Fed. R. Evid. 401. A jury could find that Garnes’s statements about his history of criminal acts, his past experiences in jail and prison, and his comfort with returning to jail would convey to a reasonable listener a sense that Garnes was willing and able to act on his violent words, and that he made those statements in a conscious attempt to make his threats to shoot and kill employees of the DOL and USPS more credible. The five statements therefore satisfy Rule 401′s relevancy test, which is a “low threshold, easily satisfied.” See United States v. Gramins, 939 F.3d 429, 450 (2d Cir. 2019). In agreement with the district court as to the relevance of the evidence, we turn to its Rule 403 analysis of probative value and potential prejudicial effect. II. Probative Value “Evidence is said to have probative value if it tends to prove or actually proves a proposition.” Jamil, 707 F.2d at 642, citing Black’s Law Dictionary 1082 (5th ed.1979). The government argues that the five statements at issue are highly probative evidence of (1) Garnes’s subjective state of mind when he made all of the allegedly threatening statements and (2) whether the communications are true threats. Turning first to whether the five statements at issue are probative of Garnes’s subjective state of mind, the government claims that Garnes’s statements about his purported criminal history demonstrate a fact distinct from his statements expressing that he might shoot someone at the USPS or DOL — specifically, that Garnes wanted the DOL employees on the phone with him to “believe that he had the capacity and the disposition to harm them and was not afraid of the consequences,” and consciously used an inflated version of his criminal history as a rhetorical tool “specifically to engender fear on the other end of the telephone.” Appellant’s Br. 25-26. The district court acknowledged that the five statements “may be probative of [Garnes's] state of mind,” but asserted that any probative value is “limited.” Garnes, 2023 WL 4489983, at *5. In support of that conclusion, the district court considered “whether an alternative piece of evidence [was available that] may carry ‘substantially the same or greater probative value but a lower degree of unfair prejudice.’” Id., quoting Old Chief v. United States, 519 U.S. 172, 182-83 (1997). It found that other statements — the admissibility of which are not challenged — are “far more probative of the elements of the charged crimes, including but not limited to [Garnes's] mens rea,” than the challenged statements are. Id. The court pointed to statements Garnes made about shooting people at the DOL and USPS, such as “somebody might get shot today coming out of the Department of Labor.” Id. at *6. Ultimately, it held that the probative value of the five statements at issue was limited because the unchallenged statements provided “ample facts” from which the government could argue that Garnes intended for his threats to be taken seriously. Id. The district court considerably misperceived the significance of the challenged evidence. We think it clear that the probative value of the five statements is substantial, and that the other alleged threats do not carry “substantially the same or greater probative value,” Old Chief, 519 U.S. at 183, as the excluded evidence. The district court is correct that in making a Rule 403 determination, a court may consider other available means of proof or “evidentiary alternatives.” Id. at 184; see also Fed. R. Evid. 403 advisory committee’s note. But the district court impermissibly extended the ruling of Old Chief in determining that substantially similar evidentiary alternatives are available in the present case; in failing to recognize that the statements at issue are not just items of evidence that can be replaced with other items of evidence, but rather may also be found to be an integral part of the charged criminal conduct itself; and in basing its exclusion of the evidence in part on its determination that the government had “ample facts” to argue from and a generally strong case. In Old Chief, the Supreme Court concluded, in a case where the defendant was charged with being a felon in possession of a firearm, that the district court abused its discretion when it rejected the defendant’s offer to stipulate to the fact of a prior conviction and allowed the government to introduce a judgment record or similar evidence that would disclose the specific felony of which the defendant had been convicted. 519 U.S. at 191-92. Although the Court acknowledged that the “prosecution with its burden of persuasion needs evidentiary depth to tell a continuous story,” it concluded that this tenet has “virtually no application when the point at issue is a defendant’s legal status,” id. at 190, and the relevance of the evidence is “solely to prove the element of prior conviction,” id. at 174. The Court could identify “no cognizable difference” in probative value between the stipulation offered by the defendant and the judgment record for the prior conviction. Id. at 191. Therefore, in the context of Rule 403, “the functions of the competing evidence [we]re distinguishable only by the risk inherent in the one [that the jury would be inflamed by the seriousness of the defendant's prior crime] and wholly absent from the other.” Id. Here, the unchallenged statements relied on by the district court and the challenged statements made by Garnes, insisting on and even exaggerating his criminal history, are not “distinguishable only by the risk inherent in the one and wholly absent from the other,” id., but are significantly different in the light they shed on Garnes’s intent. For instance, in a statement the district court found admissible, Garnes told the DOL employees: “Y’all gonna make me go to jail. I swear to God, y’all gonna make me go to jail.” Gov’t App’x 82. A jury could interpret that statement as showing that Garnes was consciously disregarding a substantial risk that his words would be construed as threats, as he was trying to make his victims think that he was serious because he understood that the consequences of his threatened actions would include incarceration. But the jury could instead conclude that Garnes was unaware of the risk that this statement would be interpreted as a threat, because he thought he was just venting his frustration about the outcome of his unemployment claim and anyone would understand that his statements were not true threats. Compare this with one of the challenged statements, uttered almost immediately after Garnes asked one of the DOL employees if the city “want[s him] to kill five or six different people” because he can’t pay his rent: “Cause listen didn’t I just tell you I got 18 and a half years in jail. It don’t bother me to be in jail.” Id. at 88. From that statement, made soon after a statement about killing people and before a prediction that he might show up on television for shooting and killing people, a jury could conclude that Garnes was aware that his communications would be perceived as threatening. Indeed, the jury might rely on the statement to adopt the government’s theory that Garnes intentionally exaggerated his criminal history to make sure that his threats were taken seriously. For similar reasons, we conclude that the five statements that Garnes made overstating his criminal history are highly probative of whether his threats to shoot USPS and DOL personnel objectively constitute “true threats,” which the government also has the burden of proving. See Black, 538 U.S. at 359 (defining a true threat as a “serious expression” of intent to harm another, as opposed to a mere hyperbolic statement). It seems obvious to us that in assessing what facially threatening words convey to the person to whom the words are directed, a threat to shoot people will have a different, and more frightening, effect coming from someone the threatened person believes — because the threatener insists on telling him — to have spent nearly two decades in a series of notorious state penitentiaries for committing multiple felonies, than the same words coming from a random person. The district court’s order of exclusion would prevent testimony from recipients of the threats about the effect that Garnes’s statements, in their totality, had on them, and the reasons for that effect, because it explicitly prohibited witnesses from mentioning the excluded statements. Because the five statements constitute evidence bearing distinctively on Garnes’s knowledge and intent when he made the alleged threats and the effect of those alleged threats on the listeners, we conclude that they were substantially probative and that the district court manifestly erred in discounting their significance.4 Further, the district court exceeded its authority to weigh evidentiary alternatives in stating that, even without the challenged statements, the government had “ample facts” from which to establish Garnes’s mens rea, because the references to Garnes’s purported criminal history conveyed distinctive probative force not conveyed by the overt threats themselves. See Old Chief, 519 U.S. at 186 (recognizing the “standard rule that the prosecution is entitled to prove its case by evidence of its own choice”); cf. Awadallah, 436 F.3d at 132-33 (considering whether there were other witnesses the government could elicit testimony from to prove an issue but noting that the government is “free to select whichever witnesses it believes will most effectively advance its case”). Accordingly, those statements should not have been excluded unless there was significant risk of unfair prejudice. See Jamil, 707 F.2d at 644; see also United States v. Dwyer, 539 F.2d 924, 928 (2d Cir. 1976) (“Since the probative value of the evidence proffered was so great, it should not have been excluded in the absence of a significant showing of unfair prejudice.”). III. Danger of Unfair Prejudice We therefore turn to the district court’s assessment of the danger of unfair prejudice. The advisory committee’s notes for Rule 403 define “unfair prejudice” as an “undue tendency to suggest decision on an improper basis, commonly, though not necessarily, an emotional one.” Evidence of other crimes that a defendant has committed, or “other-crime evidence,” can create unfair prejudice in that it can lead a jury to convict a defendant “because of his participation in the other crimes rather than because he is guilty beyond a reasonable doubt of the crime alleged.” United States v. Manafzadeh, 592 F.2d 81, 86 (2d Cir. 1979). Indeed, there is a specific Rule that expressly addresses such evidence: Rule 404(b) of the Federal Rules of Evidence prohibits a court from admitting evidence of a defendant’s other crimes or bad acts when it is proffered to show that a defendant has bad character or the propensity to commit the charged crime. Fed. R. Evid. 404(b)(1). But even under that Rule, such evidence may be admitted for other permissible purposes, such as proving intent or knowledge. Fed. R. Evid. 404(b)(2). As discussed above, “evidence must be relevant to an actual issue in the case, and its probative value on that issue must not be outweighed by its unfair prejudice to the defendant.” United States v. Mohel, 604 F.2d 748, 751 (2d Cir. 1979) (collecting cases). We have also stated that “[t]he fact that the [othercrime] evidence is in the form of statements by the defendant himself does not change the applicable analysis.” Id. at 751 n.6. In determining that the jury could not be permitted to hear Garnes’s statements about his criminal history, the district court reasoned that Second Circuit case law dictates that prior crimes evidence is always highly prejudicial, and here, the risk is even greater because the statements at issue reflect an inaccurate and exaggerated version of Garnes’s criminal history.5 Here, however, the evidence differs from most cases dealing with the prejudicial effect of evidence of a defendant’s criminal record. The point of the evidence is not that Garnes had a criminal record; it is that a jury could find that he used, and indeed exaggerated, his criminal record to intimidate his listeners and enhance the efficacy of his threats to shoot USPS and DOL personnel. The effect and intent of Garnes’s statements would be the same even if Garnes in fact had no criminal record at all — the recipients of the statements would never know the difference. The principal danger of evidence of prior crimes is the risk that the jury would draw the unfair inference that the defendant had a propensity to commit crimes, and therefore either was more likely to be guilty of the crime charged than another person as to whom the actual evidence of guilt was equally strong, or was worthy of punishment regardless of the strength of the evidence of the charged crime. In this case, however, Garnes’s claims of a dangerous criminal past are offered to support the inference that he intended to, and did, generate fear in the objects of his threats. For that reason, although we recognize that Garnes’s statements about his prior crimes may create some potential for unfair prejudice, we conclude that the five statements are part of the “res gestae, the narrative the government rightly seeks to tell at the guilt phase of a trial.” United States v. Pepin, 514 F.3d 193, 201 (2d Cir. 2008) (internal quotation marks omitted). The fact that Garnes repeated an exaggerated version of his criminal history to the DOL employees, in the course of making statements about shooting and killing employees of the DOL and USPS, may ultimately be a crucial factor for the jury in considering whether Garnes had the requisite mental state to be convicted of the charged crimes. That Garnes exaggerated his criminal history does not provide an adequate basis to exclude the substantially probative evidence when the evidence could support an inference that he did so for the purpose of making his threats more credible. The district court’s failure to appreciate that distinction caused it to overstate the risk of unfair prejudice generated by the evidence and to miscalculate the value of a limiting instruction. Unlike a case in which a jury is instructed to consider evidence of criminal conduct in the past for its relevance to intent, but not for other reasons, the government here does not seek to introduce any evidence relating to Garnes’s actual criminal history. Moreover, a limiting instruction could tell the jury not only that it should not assume that Garnes was speaking the truth about his criminal record, but also that there is no evidence before the jury as to what, if any, criminal history he has; that the jury should not speculate on that matter; that the evidence is offered only for whatever inference the jury might draw from the fact that he claimed to have the history he described; and that in fact his claims about his criminal record were inaccurate. Similarly, the government could be instructed not to suggest to the jury that Garnes had a criminal record, and to confine its use of the evidence to arguing that, even if everything he said on the subject was false, the jury should consider his claims as evidence that he was trying to instill fear, and that his claim of a serious criminal past would reasonably have had that effect on the object of his threats. For those reasons, we reject the district court’s conclusion that an instruction to the jury that Garnes’s account of his past was “inaccurate and should not be relied upon in any way for its veracity” would lead the jury to speculate about Garnes’s true criminal history and the nature of his prior convictions, thus creating an undue risk of confusing the issues, misleading the jury, and causing unfair prejudice to Garnes. Garnes, 2023 WL 4489983, at *6-7 (emphasis in original). As noted above, the district court could avoid any such problem by simply instructing the jury not to speculate on this point, and to consider the statements only for specified purposes. See United States v. Reichberg, 5 F.4th 233, 244 (2d Cir. 2021) (“ [W]e presume that juries follow limiting instructions….”) (internal quotation marks omitted). CONCLUSION We are persuaded that, in a prosecution for alleged true threats, the district court exceeded its discretion by excluding portions of the alleged threats themselves on the basis that those statements were of limited probative value that was outweighed by a substantial risk of prejudice that a jury instruction could not cure. We conclude not only that the district court incorrectly balanced the probative value and danger of unfair prejudice, but also that it incorrectly determined that other portions of the alleged threatening statements were adequate evidentiary alternatives for the five statements at issue without considering whether Garnes may have been using his criminal history as a tool to communicate the seriousness of the other alleged threats, and that a limiting instruction could not cure any prejudice. The question of the precise wording of the appropriate limiting instruction is not presented by this appeal and should be decided by the district court on remand after hearing the parties’ views. We conclude only that the district court has ample latitude to craft an instruction that would be effective in minimizing any risk that the jury would disregard the evidence and be inflamed to convict Garnes based on the belief that his (purported) past conduct showed him to be a dangerous felon. For the reasons set forth above, we REVERSE the district court’s exclusion of the five challenged statements, and REMAND the case for further proceedings.