Defendant-Appellant James J. Rbse-mond appeals a March 25, 2015 judgment entered in the- United States District Court for the Southern District of New York (McMahon, C.J.), following a jury trial, convicting him of murder for hire, conspiracy to commit murder for hire, murder through use of a firearm, and possession of a firearm, in violation of 18 U.S.C.-§§ 1958, 924(c)(l)(A)(iii), and 924(j). Rosemond was the head of Czar Entertainment, a music label that engaged in a lengthy and violent feud with a rival company, Violator Records, and its rap group, G-Unit. The feud culminated in the fatal shooting of a G-Unit associate, Lowell Fletcher,
Following his arrest for narcotics-related charges, Rosemond participated in proffer sessions with the Government in hopes of reaching - a cooperation- agreement. Rosemond and the Government signed a proffer agreement that prohibited the Government from using Rosemond’s statements against him, except to rebut factual assertions made by him or on his behalf at a later proceeding. During one such proffer session, law enforcement officers asked Rosemond if he knew that his and- his associates’ actions in September 2009 would lead to Fletcher’s death, Rosemond responded that he knew Fletcher would die.
At Rosemond’s first trial for his role in Fletcher’s murder, the district court ruled that any argument by defense counsel that the Government had failed to prove that Rosemond had intended to murder—as opposed to merely shoot—would open the door to admitting his proffer statement. The first trial resulted in a mistrial, and at the second trial the district court adhered to its prior rulings as to the proffer statements. As a consequence, Rosemond limited his defense. He was convicted on all counts.
On appeal, Rosemond contends that 1) the district court erred in ruling that certain defense arguments would open the door to the admission of statements made during a proffer session; 2) the district court erred in admitting evidence of prior bad acts; and 3) there was insufficient evidence to support the conviction. We conclude that the district court erred in unduly restricting Rosemond’s ability to defend against the charges, and that such error was not harmless. Accordingly, we vacate the judgment and remand for a new trial.
BACKGROUND
I. The Facts
Because Rosemond appeals his convictions following a jury trial, “our *100statement of the facts views the evidence in the light most favorable to the government, crediting any inferences that the jury might have drawn in its favor.” United States v. Dhinsa, 243 F.3d 635, 643 (2d Cir. 2001) (quoting United States v. Salameh, 152 F.3d 88, 107 n.1 (2d Cir. 1998) (per curiam)). At trial, the Government elicited testimony from three cooperating witnesses—Khalil Abdullah, Mohammed Stewart, and Brian McCleod—about the violent hip hop feud between Czar Entertainment and G-Unit and the events leading up to Fletcher’s death.
A. The Feud
Rosemond was the owner of Czar Entertainment, a music business that represented and managed various hip hop and rap musicians, including rap artist Jayceon Taylor. Czar had a longstanding and violent rivalry with Violator Records and its rap group, G-Unit, featuring Curtis Jackson, Marvin Bernard, and Lloyd Banks. The dispute arose in part after Jackson publicly insulted Taylor on Hot 97, a New York hip hop radio station, in February 2005. After hearing what was said on the radio, Rosemond told his associate, Mohammed Stewart, to accompany Taylor to Hot 97 to “make sure nothing happen[ed] to him.” App. 309. When Taylor arrived at Hot 97, someone started shooting into the crowd outside the radio station. Taylor’s friend was shot in the leg. Later that day, Stewart had another Czar associate shoot up the front door of Violator Records. Rosemond paid Stewart $2,000 for that shooting.
Rosemond had another altercation with G-Unit in December 2006 at an award ceremony at the Apollo Theater in Harlem. Marvin Bernard of G-Unit confronted Rosemond at the event about Taylor “talking reckless” about G-Unit frontman, Curtis Jackson. App. 258. In anticipation of a shooting, Rosemond left through a side exit with his associates, including Khalil Abdullah. After they left the Apollo, Rose-mond and Abdullah followed Bernard’s car and shot fifty rounds into it when it pulled over. Following the Apollo incident, a meeting was organized by music industry mogul, Sean Combs, between Rosemond and G-Unit’s manager, Christopher Lighty, to make peace between the groups. The meeting got heated and resulted in Rosemond getting “mushed in the face” by Lighty. App. 260. Rather than quell the feud, the meeting only increased tensions between the groups.
B. Assault of Rosemond’s Son and Subsequent Retaliation
On March 20, 2007, three G-Unit associates—Marvin Bernard, Jaleel Walter, and Lowell Fletcher—were leaving Violator’s office when they saw a 14 year-old boy wearing a sweatshirt bearing the Czar Entertainment logo. They confronted him, pushed him up against a wall, slapped him, and threatened him with a gun. A parking attendant at the garage across the street saw what was happening and yelled at them to break it up. The G-Unit associates got into a black Suburban and drove away.
The boy was Rosemond’s son. When Rosemond found out about the incident later that day, he was furious and immediately sent Stewart to cut a G-Unit associate with a razorblade. Stewart testified that Rosemond was so disturbed by the attack on his son that he sought to retaliate in “three ways”: “through the law, through music and through streets.” App. 315.
Rosemond first sought out assistance from law enforcement. Rosemond’s son reported the incident to the police and identified Fletcher and Bernard as his attackers. Criminal charges were brought against them both. Fletcher eventually *101pled guilty to assault and endangering the welfare of a child, and began serving a term of imprisonment in Mohawk Correctional Facility. Next, ■ on. the musical front, Rosemond organized conferences with hip hop figures to “talk about the guns and violence in hip-hop.” App. 315. Taylor also wrote a song about the feud.
The real retaliation, however, was achieved through “violence in the streets” where “[t]he objective was to shoot somebody.” App. 315. Violence between the two gangs began to ratchet up. A month after the slapping incident, in April 2007, Rose-mond claimed to have shot thirty rounds into Bernard’s mother’s house in Queens. Over the next couple of years, he and his associates continued to target G-Unit members. For instance, Stewart threw Molotov cocktails at and shot rounds into G-Unit associate Walter’s house and car in Staten Island, and another Czar associate was paid $5,000 for having a G-Unit jeep torched in New Jersey. There were various unsuccessful' attempts to shoot Bernard, Walter, Lighty,- and their homes, cars, and family members by Rosemond, Stewart, and other. Czar associates. At one point, after spotting G-Unit members enter a van, Rosemond “tried to make it a coffin” by shooting it up. App. 320.
Stewart testified to statements made by Rosemond during this time, including “something like they’re not going to understand what it is until they’re carrying a coffin.” App. 315.
C. The Fletcher Murder
Meanwhile, Fletcher—one of the assailants of Rosemond’s son—was serving his state sentence at Mohawk Correctional Facility, where his presence came to the attention of another inmate, Brian McCleod. Unbeknownst to Fletcher, McCleod was a friend of Rosemond. McCleod and Rosemond had spent time in jail together in the late 1990s and worked together in the music and drug business after they' were released. McCleod had been serving a New York state prison term for possession of cocaine he removed from a stash house at Rosemond’s behest in 2004.
On August 10, 2009, McCleod was released on parole. Shortly thereafter, he met with Rosemond and told him that he “had a line on [ie., had access to] ... the individual [who] slapped [Rosemond’s] son,” referring to Fletcher. App. 480. In response, Rosemond said that “since his son had been assaulted, he hadn’t been able to sleep,” and that he had been “hitting them everywhere they turn,” including shooting their cars in front of the Apollo, blowing up their cars in South Beach, and shooting their homes. App. 481. Rosemond told McCleod that he wished he had known where Fletcher was incarcerated earlier, as he would have paid $10,000 “for anybody who would have marked him, who would have scarred him,” meaning “[t]hat he would have paid someone [that amount] to cut” Fletcher. App. 482. . .
Rosemond met McCleod a week later and told him that he would pay $30,000 to anyone who “could bring [Fletcher to] him.” App. 485. Rosemond said he would “hit him so fast and so hard, he’s not even going to realize it’s coming.” App. 486. He “was talking about shooting” Fletcher. Id. McCleod suggested involving Derrick Grant, a trusted associate. Rosemond agreed. The next day, McCleod went to see Grant and told him that Rosemond “had 30,000 for anybody who would bring [Fletcher] to him.” App. 490. Grant agreed to be the shooter.
Later that week, McCleod learned from a source that Fletcher was soon to be released from prison and had already been transferred to Queensboro, a temporary holding facility for those about to be re*102leased. McCleod informed Rosemond,- who told McCleod to get in touch with Grant and Jason Williams, Rosemond’s chauffeur. On September 11, 2009, McCleod and Williams drove to Queensboro, contemplating the possibility that “if something could happen,” they would “maybe even-do the deed that day,” meaning “[t]he shooting.” App. 494. When they arrived, however, McCleod learned, that Fletcher had already been released. McCleod instead reached Fletcher by phone and “welcomed him home.” App. 502. During that phone call, McCleod suggested that they “get together, talk it up, get with some girls, [and] have some drinks” in the “near future.” App. 502. He also indicated that he had some money to give Fletcher to help him get on his feet. This was all to “artificially aid the relationship” to get Fletcher to “trust” him and “have an expectation and a reason to speak to [McCleod] in the future.” App. 503.
Later that month, Rosemond instructed Williams to give McCleod money to buy a new, temporary phone to be used exclusively for speaking with Fletcher. Rose-mond asked McCleod if he could “handle the actual deed, , the actual act of bringing Lowell. Fletcher to a location, shooting Lowell Fletcher,” because, if not, he could get someone else to do it. App. 506-07. McCleod assured him that “[e]verything’s good.” App. 507.
At some point during this period, Rose-mond told Abdullah about how he had McCleod “line [Fletcher] up for when he get home” and that “these dudes ain’t gonna be happy until they go to a funeral.” App. 266.
On September 25, 2009, McCleod again met with Rosemond. Rosemond showed McCleod on his Blackberry what he had been told was Fletcher’s address in the Bronx to determine whether it “would ... be a good location to .., actually have the shooting.” App. 512. They agreed that McCleod would go to the address to see if it was a suitable location for a shooting, and report back to Rosemond. A code was created: if McCleod thought the location was safe, he would tell Rosemond, “I got with the girl, I like her”; if he did not, he would say, “I don’t like her, not good chemistry.” App. 515. Once he visited the building on West 161st Street in the Bronx, McCleod saw “cameras everywhere,” and testified that he texted Rose-mond back saying, “no, I don’t like the girl, no chemistry.” App, 517.
On September 26, 2009, McCleod, Williams, and Grant went out looking for a better location for the-shooting. They settled on a dark, quiet area near the 4 Train station on Mount Eden Avenue in the Bronx. McCleod arranged to meet Fletcher there the following evening. He sent Rosemond a text that said, “I got a hot date,” to which Rosemond responded, “OK. Have fun.” App. 539.
The next day, before Fletcher was expected to arrive, McCleod and Williams met Grant at the agreed-upon location on Mount Eden Avenue. Rosemond had also sent two other Czar associates—Rodney Johnson and Shawn Williams—to serve as backup. McCleod and Fletcher then exchanged a series of phone calls as McCleod sought to lure Fletcher to the spot where Grant was waiting for him. McCleod told Grant—the gunman—to take his position. When the time came, Grant shot Fletcher five times in the back using a silencer and gun provided to him by Rosemond. .Fletcher died shortly thereafter. In return, Rose-mond paid McCleod and Grant with a kilogram of cocaine, worth approximately $30,000.
After Fletcher’s death, Rosemond told Abdullah what had transpired, saying, “Yo, the bitch is out of here” and “dude checked out.” App. 267-68.
*103D. Rosemond’s Arrest and Proffer Session
Prior to the indictment in this case, Rosemond was arrested and prosecuted for narcotics-related offenses in the Eastern District of New York.1 In response to those charges, Rosemond participated in proffer sessions with the Government in hopes of reaching a cooperation agreement. A proffer agreement was executed, stipulating that the Government would not use any of Rosemond’s statements made during the proffer sessions against him, except that they could be used “as substantive evidence to rebut, directly or indirectly, any evidence offered or elicited, or factual assertions made, by or on behalf of [Rosemond] at any stage of a criminal prosecution.” App, 212.
During one such proffer session, “Rose-mond was asked if he understood that, as a result of the actions he took with others in September 2009, Lowell Fletcher would be killed.” App. 204. The notes taken during the proffer session state that Rosemond “responded affirmatively” and “knew [Fletcher] was going to be dead.” Id.
II. The Proceedings Below
A. The First Trial
A seven-count indictment was filed against Rosemond and his co-defendant, Rodney Johnson, charging them both with conspiracy to commit murder for hire, murder for hire, murder through use of a firearm, and possession of a firearm during murder for hire. Only Johnson was named in the remaining counts of the indictment, which related to the drug conspiracy and were substantially the same as the charges Rosemond had already been convicted of and sentenced for in the prior proceeding. A joint trial was held.
Brian McCleod testified for the Government as a cooperating witness. During the Government’s direct examination, McCleod testified that Rosemond had never used the words “murder” or “kill”, in connection with Fletcher. He also testified that he had previously told the prosecutors that he “did not think this was going to be a murder,” and that he “knew there was going to be a shooting,” but “was telling [himself] nobody was going to get killed.” App. 176. Defense counsel thoroughly examined .this subject on cross-examination, emphasizing that McCleod had previously told the prosecutors that he believed he was participating only in a shooting, not a murder. McCleod admitted that he had repeatedly told prosecutors that he did not believe a murder would take place.
Defense counsel also asked McCleod if Rosemond had ever in fact told McCleod to murder Fletcher prior to the shooting. McCleod admitted that he had never discussed “murdering” or “killing” Fletcher with either Rosemond or Grant. His cross-examination included the following exchanges:
Q. While we’re on that, Mr. Rosemond never told you that he wanted you to murder Lowell Fletcher, correct?
A. No, sir.
Q. Mr. Rosemond never told you that he wanted you to enter into a conspiracy to murder Lowell Fletcher, did he?
A. No one talks like that. No, sir.
Q, Well, I don’t know about no one, but certainly in this case, Mr. Rose-*104mond never used those words, never said those words to you in any of the meetings he had with you. Yes or no, isn’t that correct?
A. He never used those words. No, sir.
App. 188.
Q. Did you say to Mr. Grant, hey, listen, there is $30,000 on the table for us to kill Lowell Fletcher? Did you say anything like that to Derrick Grant back at that time? Yes or no, Mr. McCleod.
A. No, sir.
App. 188.
Q. Incidentally, up to this point, where you’re on Mount Eden Avenue, as we have it from your direct testimony, you had no conversation with Mr. Rosemond about murdering. Mr. Rosemond never asked you to murder Lowell Fletcher, correct?
A. No, he did not.
Q. In fact, you had had no conversation up to this point with Derrick Grant about murdering Lowell Fletcher, had you?
A. No, I had not.
Q. In fact, you had no conversation with Rodney Johnson or Jason Williams about murdering Lowell Fletcher, isn’t that true?
A. That is true.
App. 190.
The Government submitted a letter brief the next day, asserting that defense counsel’s questioning opened the door to Rose-mond’s proffer statements because it implicitly argued that “Rosemond did not intend to have Fletcher murdered.” App. 204. For the same reason, the Government took issue with defense counsel’s opening, which included a statement that McCleod would testify that he “didn’t know it was a murder; Jim Rosemond never told [him] to murder anybody.”2 App. 205. The Government argued that while questions solely focused on impeaching McCleod with his prior inconsistent statements did not open the door to the proffer statement, other questions “were posed in order to elicit answers indicating that no mention of ‘murder’ or ‘killing’ had been made.” App. 210. The “only conceivable purpose” of these questions, according to the Government, was to “imply to the jury that, in fact, Rosemond is not guilty of Counts One through Four of the Indictment because Rosemond did not intend to participate in a murder.” Id.
The trial court heard argument the next morning and ruled from the bench that afternoon. A written ruling was issued later that day. The trial court concluded that the questions limited to prior statements were acceptable forms of impeachment with a prior inconsistent statement, but that the other questions—focusing on the fact that Rosemond did not actually use the words “murder” or “kill”—triggered Rosemond’s proffer agreement waiver because they implicitly asserted that the object of the conspiracy was something less than murder. The trial court declined, however, to admit the proffer statement, to avoid a Bruton problem for Rosemond’s co-defendant, Rodney Johnson. The court made clear that if the trial involved Rose-mond alone, it would have admitted the proffer notes. Instead, the court decided to “cabin” Rosemond’s closing argument as follows:
*105[Defense counsel] can certainly attack the credibility of Mr. McCleod on the ground that he has given inconsistent statements in the past, and the jury will be carefully .instructed on the prior inconsistent statement rule. He can argue in general terms that the Government has not proven all or certain of the elements of the charged crimes beyond a reasonable doubt. He can argue that the Government’s proof fails to establish beyond a reasonable doubt the existence of a conspiracy, for example, because its evidence comes out of the mouths of admitted liars. What he cannot do is argue that the Government has failed to prove that the object of the conspiracy and the intent of Rosemond was to murder Lowell Fletcher, as opposed to simply shooting him, or assaulting him, or doing violence to him. That argument is inconsistent with a factual assertion made during his proffer, and so is not available to him.
App. 238 (emphasis added). Defense counsel so cabined his argument, focusing instead on the cooperating witnesses’ motive to lie.
The jury was unable to reach a verdict on the murder for hire charges against either defendant. The court declared a mistrial.
B. The Second Trial
A second trial was held as to Rosemond alone on the same charges. Prior to cross-examining McCleod, defense counsel sought to clarify the permissible scope of his questions so as to not “repeat what took place at the last proceedings.” App. 659. Defense counsel then stated his interpretation of the district court’s prior ruling, that is, that he could elicit only prior inconsistent statements. The Government “agree[d] with that interpretation, as long as [defense counsel] d[id] not argue in summation that this was merely a shooting based on those answers.” Id. The district court also agreed, stating that defense counsel would be “entitled to examine, as indeed the prosecutor examined, about the statements that were or were not made.” App. 659-60.
During McCleod’s testimony, he was not asked—either on direct examination by the Government or on cross-examination by defense counsel—about his prior statements to prosecutors or whether Rose-mond used the words “murder” or “kill” when discussing the Fletcher shooting.
During redirect, the prosecutor asked McCleod how he came to the realization that Fletcher was murdered, rather than “merely shot.” App. 681. McCleod answered as follows:
A: ... [T]his is much too much planning for just a simple shot.
Q: In any conversation you had with James Rosemond, did he ever say to you, Don’t kill Lowell Fletcher?
A: Mr. Rosemond never mentioned killing Fletcher at all.
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Q: Why did you tell the government on [previous] occasions that this was a shooting?
A: The first time and even up until now I just—I had some very serious issues with admitting to myself that I participated in the murder of another man to [sic] looks like me, especially considering my family history.... I guess I felt guilty. My mother’s going through it. My brother was murdered. He was shot. And here I am doing the exact same thing.
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Q: What words did Rosemond use when he was talking to you about what to do to Lowell Fletcher?
*106A: Well, ... initially he just said he was going to hit him so hard and so fast he wasn’t going to see it coming ■And after that, it was, Am I sure I can handle it? Am I sure that Derrick, and I can handle it on our own?
App. 682-83. Defense counsel did not recross McCleod about his prior statement about not knowing that a murder was to occur.
Again, prior to summation, the court reiterated its ruling that Rosemond could not argue that “this was a mere shooting” because they had “been through that.” App. 703 (“Been there; ■ done that. If the argument is made, we will stop; we will read the proffer agreement; and then we will pick up and move on. The one advantage to having a do-over is that [defense counsel] hav[e] been through this once before, and have, I think, been very careful....”).
This time, the jury convicted Rosemond on all counts. He was sentenced to life plus 20 years, consisting'.of concurrent mandatory life terms on the murder for hire and murder for hire conspiracy convictions, and two additional consecutive ten-year terms on the firearms charges. 18. U.S.C. §§ 924(c), 0).
This appeal followed.
DISCUSSION
Three issues are presented: (a) the interpretation of Rosemond’s proffer agreement; (b) the admission of uncharged acts; and (c) the sufficiency of the evidence on the element of intent. Because we vacate Rosemond’s conviction on the ground that the district court improperly interpreted the scope of his proffer agreement waiver, we do not reach Rosemond’s second argument. As to the third issue, we conclude that there was sufficient evidence to support Rosemond’s conviction, and therefore decline to direct the district court to enter a judgment of acquittal.
I. The Proffer Agreement Waiver
Rosemond argues that the district court’s rulings during the first trial—which extended to the second—unduly restricted the permissible scope of his lawyer’s argument and questioning of witnesses, in violation of the Sixth Amendment. We agree, and conclude that the error was not harmless.
A. Waiver
As a preliminary matter, the Government contends that Rosemond has waived this argument absent any plain error by failing to renew his objection at the second trial. The contention fails. Where a defendant has made his position clear, further objections to “rulings or orders of the court are unnecessary” to preserve a claim of error for appellate review. Fed. R. Crim. P. 51(a); see Thomley v. Penton Publ’g, Inc., 104 F.3d 26, 30 (2d Cir. 1997) (“Because [plaintiff] argued its position to the district judge, who rejected it, a further exception after [the ruling] would have been a mere formality, with no reasonable likelihood of convincing the court to change its mind on the issue.”); United States v. Lewis, 823 F.3d 1075, 1082 (7th Cir. 2016) (“[T]here is no need for a party to state an ‘exception’ to a court ruling that has already been made.”). The purpose of the appellate waiver rule is “to induce the timely raising of claims and objections, which gives the district court the opportunity to consider and resolve them.” Puckett v. United States, 556 U.S. 129, 134, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009).
The trial court was given such an opportunity here. As discussed above, the issue was fully litigated during the first trial and resulted in a ruling by the district court. *107At the second trial,; the court stated that its prior rulings remained in effect. The Government argues, that the district court was not given an opportunity to revisit its prior rulings given the different context .of the new trial, but does not point to any change in circumstances that, would have had a material effect on the -trial court’s decision had it been brought to its attention. Thus, taking further exception under the circumstances would have been futile. See Rose v. N.Y.C. Bd. of Educ., 257 F.3d 156, 160 (2d. Cir. 2001).
B. Applicable Law
Under Rule 410 of the Federal Rules of Evidence, “a statement made during plea discussions with an attorney for the prosecuting authority if the discussions did not result in a guilty plea” is not “admissible against the defendant who made the plea or participated in the plea discussions.” Fed. R. Evid. 410(a)(4); see also Fed. R. Crim. P. 11(f) (“The admissibility or inadmissibility of a plea, a plea discussion, and any related statement is governed- by Federal Rule of Evidence 410.”). The protections of Rule 410, however, may be waived so long as the defendant agrees to the waiver knowingly and voluntarily. United States v. Mezzanatto, 513 U.S. 196, 209-10, 115 S.Ct. 797, 130 L.Ed.2d 697 (1995). In Mezzanatto, the Supreme Court deemed enforceable a waiver provision allowing the Government to use a defendant’s statements made during plea negotiations to impeach him when he testified in a manner inconsistent with those statements. Id. at 198-99, 115 S.Ct. 797.
We considered a more expansive waiver in United States v. Velez, one that allowed the Government to introduce the plea negotiation statements not only when the defendant testified inconsistently, but also when the defense presented contradictory other evidence or even arguments. '354 F.3d 190,195 (2d Cir. 2004). We concluded that “fairness dictates that the agreement be enforced” according to its terms, notwithstanding the disparity in bargaining power. Id. at 196 (“If the proffer agreement is not enforced, a defendant will have less incentive to, be truthful, for he will know that his proffer statements cannot be used against him at trial as long as he does not testify, even if he presents inconsistent evidence or arguments.” (quoting United States v. Gomez, 210 F.Supp.2d 465, 475 (S.D.N.Y. 2002))); see also United States v. Krilich, 159 F.3d 1020, 1026 (7th Cir. 1998).
Proffer agreements are contracts to be interpreted according to ordinary principles of contract law. United States v. Liranzo, 944 F.2d 73, 77 (2d Cir. 1991). Like all contracts, proffer agreements must be interpreted “to give effect to the intent, of the parties.” United States v. Barrow, 400 F.3d 109, 117 (2d Cir. 2005) (quoting Liranzo, 944 F.2d at 77). We consider the district court’s interpretation of the scope of a proffer agreement waiver de novo and its evidentiary rulings for abuse of discretion. Barrow, 400 F.3d at 117.
In determining whether a defendant has triggered the type of waiver contained in Rosemond’s proffer agreement, we ask first whether there has been any evidence offered or elicited, or “factual assertion” made, by or on behalf of the defendant that would trigger the Rule 410 waiver, and second, if so, whether the proffer statement “fairly rebut[s]” the fact asserted or evidence offered or elicited. See Barrow, 400 F.3d at 117-21. If the defendant makes a factual assertion at trial that contradicts a statement made during the proffer session, the Government may then offer the earlier proffer statement to rebut the assertion being made at trial. Id. at *108120. Rebuttal is “necessarily a flexible concept,” id. and not “limited to evidence that directly contradicts what it opposes; rath■er, rebuttal encompasses any evidence that the trial judge concludes fairly counters and casts doubt on the truthfulness of factual assertions advanced, whether directly or implicitly, by an adversary,” id. at 121.
In United States v. Barrow, we held that a waiver provision substantially similar to the one in this case applied to any factual assertions made by or on behalf of the defendant, whether made “directly or implicitly,” during counsel’s opening argument or through cross-examination. 400 F.3d at 119. We made clear, however, that “[t]he mere fact that a defendant pleads not guilty and stands trial is not a factual assertion that triggers the proffer agreement waiver.” Id. at 118. Defense counsel may also “attempt to demonstrate why the facts put in evidence by the prosecution are insufficient,” and “challenge[ ] the sufficiency of government proof on elements such as knowledge, intent, identity, etc.,” without triggering the factual assertion requirement of the waiver. Id. at 119. In other words, the proffer agreement does not bar a defendant from arguing that the Government has failed to meet its burden of proof.
We reiterated this rule in United States v. Oluwanisola, concluding that defense counsel must be permitted to “draw the jury’s attention to the lack of evidence” presented on specific elements without triggering the waiver. 605 F.3d 124, 132 (2d Cir. 2010). There, we vacated a conviction where defense counsel was precluded, except to an extent in summation, from arguing that specific elements had not been proven without triggering the proffer waiver. Id. To hold otherwise, we explained, would prevent defense counsel from challenging the Government’s lack of evidence on a particular element, even where the Government “failed to introduce any evidence on a certain element.” Id.
The line between challenging the sufficiency of the Government’s evidence and implicitly asserting new facts can be a fíne one. See United States v. Roberts, 660 F.3d 149, 158 (2d Cir. 2011) (admitting that this “distinction is more easily stated than applied”). When the defense introduces an exhibit or offers testimony of a defense witness, there is a greater likelihood that new facts are being asserted. See id. at 163 (concluding that the waiver provision was triggered when defense counsel “put documentary evidence before the jury to imply facts that contradicted the defendant’s proffer statements”). But “[pjarticular caution is required when the purported fact is asserted by counsel rather through witness testimony or exhibits.” Id. at 158. In evaluating defense arguments and questions, we have advised district courts to “consider carefully what fact, if any, has actually been implied to the jury before deciding whether proffer statements fairly rebut it.” Barrow, 400 at 119; accord Oluwanisola, 605 F.3d at 132.
This distinction is illustrated by our treatment of cross-examination questions that attack a witness’s credibility. On the one hand, defense counsel may cross-examine a witness “in a way that cast[s] doubt on his credibility,” Roberts, 660 F.3d at 163, as well as “challengfe] a witness’s perception or recollection of an event,” Barrow, 400 F.3d at 119. Such attacks “do[ ] not necessarily imply that the event did not occur, only that the witness may not have seen or reported it accurately,” and thus primarily implicate the Government’s burden of proving each element beyond a reasonable doubt. Id.; see also Krilich, 159 F.3d at 1025-26. For example, in Oluwanisola, defense counsel asked a series of questions implying that a cooper*109ating witness was fabricating his testimony that he saw the defendant perform certain incriminating acts. 605 F.Bd at 132. We held that such questioning should not be construed as an implicit factual assertion that the defendant did not actually perform those incriminating acts. Id. at 133 (“There is no inconsistency, or contradiction between a defendant’s admission that he robbed the bank and his challenge to a witness’s testimony that the witness saiv the defendant rob the bank and recognizes the defendant.”).
On the other hand,' questions “accusing a witness of fabricating an event” can implicitly assert that the event did not take place, and may; depending on the context, satisfy the factual assertion requirement. Barrow, 400 F.3d at 119 (emphasis added). In Barrow, defense counsel affirmatively argued during opening statements that the defendant had been mistaken for someone else and that the true culprit was the cooperating witness’s brother. Defense counsel then accused that Government witness during cross: “You made up about meeting the [confidential informant] there that day, didn’t you?” Id. at 114. There, in light of his opening statement, defense counsel’s question implicitly asserted that no meeting in fact took place “because his theory of mistaken identity depended on that fact.” Olmvanisola, 605 F.3d at 133 (discussing Barrow).
To be sure, implicit in questions and arguments regarding witness fabrication, perception, or recollection will often be the claim that the event did not occur the way the Government suggests. Absent an affirmative assertion of fact contradicting the proffer agreement, however, such questions will usually be insufficient to trigger the “factual assertion” requirement of the proffer waiver.
To summarize, the following are not factual assertions sufficient to trigger the waiver provision in a proffer agreement:
• pleading not guilty, see Barrow, 400 F.3d at 118; Krilich, 159 F.3d at 1025;
• arguing generally that the Government has not met its burden of proof, see Barrow, 400 F.3d at 119;
• arguing specifically that the Government has failed to prove particular elements of the crime, such as intent, knowledge, identity, etc., see id. at 119;
• cross-examining a witness in a manner to suggest that he was lying or mistaken or was not reporting an event accurately, see Oluwanisola, 605 F.3d at 132-33; Barrow, 400 F.3d at 119; Krilich, 159 F.3d at 1025 (“Impeachment of a witness need not be ’contrary to’ or ’inconsistent with’ a defendant’s admission of guilt in a bargaining proffer.”);3
• cross-examining a police officer about discrepancies between his testimony and his earlier written report, see Barrow, 400 F.3d at 115,119; and
• arguing that the Government failed to present corroborating evidence, see Roberts, 660 F.3d at 158-59.
The following are factual assertions that will trigger the waiver:
• asserting, in an opening statement, that someone other than the defendant was the real perpetrator of the crime, see Barrow, 400 F.3d at 114,119;
• accusing an officer, in cross-examination, that he had fabricated a meeting with a confidential informant where defense counsel had argued mistaken iden*110tity in his opening statement, see id.; see also Oluwanisola, 605 F.3d at 132-33;
• arguing that a shooting was “an intended kidnapping gone wrong,” when the defendant admitted in a proffer session that the shooting was “an intentional murder,” Gomez, 210 F.Supp.2d at 472 (noted with" approval in Velez, 354 F.3d at 195-96); and
• proffering documentary evidence that implied that a cooperating witness was not present as alleged by the Government, where the evidence was offered not just to impugn the witness’s credibility, but to prove a fact that contradicted the defendant’s proffer statement, see Roberts, 660 F.3d at 163-64.
C. Application
Rosemond’s proffer agreement contained a waiver that allowed his statements to come in as evidence “to rebut, directly or indirectly, any evidence offered or elicited, or factual assertions made, by or on behalf of [Rosemond] at any stage of a criminal prosecution.” App. 212.
The proffer statements at issue were 1) Rosemond’s positive response after being asked whether he “understood that, as a result of the actions he took with others in September 2009, Lowell Fletcher would be killed”; and 2) Rosemond’s admission that he “knew [Fletcher] was going to be dead.” App. 204.
We conclude that the district court erred in circumscribing both defense counsel’s argument and his cross-examination of McCleod.
i. Scope of Defense Counsel’s Argument
The district court interpreted Rosemond’s proffer waiver to prohibit any implicit argument that “the Government has failed to prove that the object of the conspiracy and the intent of Rosemond was to murder Lowell Fletcher, as opposed to simply shooting him, or assaulting him, or doing violence to him,” as that argument “is inconsistent with the factual assertion made during his proffer.” App. 238. This ruling is at odds with our decisions in Barrow and Oluwanisola, both of which clearly allow defendants to argue that specific elements of the crime have not been proven. See Oluwanisola, 605 F.3d at 132; Barrow, 400 F.3d at 119.
Rosemond should have been permitted to argue, without triggering the proffer waiver, that the Government failed to prove that he intended to murder Fletcher. See Barrow, 400 F.3d at 119 (defense counsel may “challenge[ ] the sufficiency of government proof on elements such as ... intent” without triggering the proffer waiver); Oluwanisola, 605 F.3d at 132 (“Under Barrow, [defense counsel] should have been permitted ... to reference certain elements of the crime and argue that the government would be unable to sustain its burden of proof as to those elements.”). There is a material difference between the statement “the Government’s evidence fails to establish that Rosemond intended that Fletcher be murdered, as opposed to shot or injured,” and asserting as fact that “the object of the conspiracy was to non-fatally assault Fletcher”; only the latter is a factual assertion that would trigger the waiver. Defense counsel never attempted to affirmatively argue or prove that Rose-mond conspired to commit only a nonfatal shooting. Cf. Roberts, 660 F.3d at 162 (finding waiver triggered where defense introduced flight logs and swipe-card records to “urge .,. a factual inference” that Government’s witness was in fact elsewhere); Barrow, 400 F.3d at 119 (concluding that “statement of fact in a defense opening ... unequivocally identifying [a different person] as the real perpetrator of the charged crimes” triggered the waiver’s *111“factual assertion” requirement); United States v. Hardwick, 544 F.3d 565, 570-71 (3d Cir. 2008) (concluding that cross-examination insinuating that different drug gang had particular motive to kill victim triggered proffer agreement waiver). Notably, unlike the statement “Rosemond intended to commit a non-fatal shooting,” the argument that there is insufficient evidence of intent to murder suggests no new facts and injects no alternate version of events inconsistent with the proffer statements. See Roberts, 660 F.3d at 158 (“[Arguments or questions challenging ‘the sufficiency of government proof,’ ... ‘without a factual assertion contradicting facts admitted in the proffer statement,’ do not trigger a waiver provision.” (quoting Olu-wanisola, 605 F.3d at 133)).
The Government contends that implicit in the argument that there was insufficient evidence of intent to murder is the factual assertion that Rosemond did not actually intend to murder Fletcher. Challenges to the sufficiency of the Government’s evidence, however, will often carry with them the inference that events did not actually occur consistent with the Government’s theory, and thus—at some level—are arguably contrary to the proffer statements. The same is true when a defendant enters a plea of “hot guilty,” but these are not “factual assertions” as they do not propose an alternate version of events inconsistent with the proffer statement.
Defense counsel was also entitled to argue that certain inferences from the Government’s proof should not be drawn. For example, the Government argued that an intent to murder should be inferred from certain statements made by Rosemond, such as “[he would] hit [Fletcher] so fast and so hard, he’s not even going to realize it’s coming,” App. 486, and “these dudes ain’t , gonna be happy until they go to a funeral,” App. 266. Defense counsel should have been permitted to challenge these types of inferences by “attempting] to demonstrate why the facts put in evidence by the prosecution [were] insufficient to permit the jury to find the elements of the crime proved.” Barrow, 400 F.3d at 119. Defense counsel was entitled to argue that McCleod’s testimony that he never heard Rosemond use the words “murder” or “Mil” undercut the Government’s assertion that Rosemond intended to murder without triggering the waiver. Just as the suggestion that a witness did not see the defendant rob the bank is not inconsistent with the defendant’s admission that he robbed the bank, Oluwanisola, 605 F.3d at 133, McCleod’s testimony that he never heard Rosemond say “murder” or “kill” is not inconsistent with Rosemond’s admission during the proffer session that he knew Fletcher would die.
ii. Scope of Defense Counsel’s Cross-Examination
Likewise, defense counsel’s questions that probed the already elicited fact that McCleod never heard Rosemond use the words “MU” or “murder” were within bounds. The district court found that the questions “implied that Rosemond did not participate in a murder conspiracy or order the murder of Lowell Fletcher[,] ... that any agreement to do violence to Lowell Fletcher was at best an agreement to commit a non-fatal shooting of Fletcher (and thus not an agreement to commit a murder-for-hire as charged), and that Rosemond never intended for Fletcher to be killed.” App. 236. These questions, it concluded, were implicit factual assertions that “directly contradicted] Rosemond’s proffer that he knew Fletcher would be Mlled :\Id.
We disagree; The questions at issue attacked the Government’s proof without asserting any new facts. Rosemond’s admis*112sion that he knew Fletcher would be dead is not inconsistent with McCleod’s testimony that the words “kill” and “murder” were not used in their discussions, and the Government offered other proof of that intent. See Oluwanisola, 605 F.3d at 133 (explaining that witness fabrication of an event does not necessarily imply that the event did not occur). Rosemond could have intended the shooting to be a murder without saying as much to McCleod or using those specific words before the fact. Indeed, the Government’s theory rests on that very scenario. See Appellee’s Br. 35-36 (“The factual assertion implied by the Government .,. was that, notwithstanding the prior inconsistent statements by McCleod, it became clear to McCleod that Rosemond intended for Fletcher to be killed as part of the attack McCleod was hired to carry out, which is entirely consistent with Rosemond’s proffer statement.”). Such inquiry into exculpatory facts already elicited by the Government did not trigger the waiver. See Barrow, 400 F.3d at 119 (“[D]efense arguments that attempt to demonstrate why the facts put in evidence by the prosecution are insufficient to permit the jury to find the elements of the crime proved [are not factual assertions that trigger the proffer agreement waiver].” (emphasis added)). Drawing the jury’s attention to the fact that McCleod did not discuss killing or murdering in those words with Rosemond was simply an attempt to highlight the supposed insufficiency of Government proof on the element of intent.
Again, and most importantly, defense counsel did not accuse McCleod of actually conspiring with Rosemond to commit a non-fatal shooting, or make factual assertions to that effect. To the extent the questions might also have carried the implication that Rosemond did not actually intend to have Fletcher murdered, they were no more inconsistent with the proffer waiver than entering a plea of not guilty or challenging the sufficiency of the evidence.
As the district court correctly ruled, questions challenging the credibility of a witness do not trigger the waiver provision absent factual assertions contradicting the proffer statement. See Roberts, 660 F.3d at 158. Thus, it was permissible for defense counsel to ask questions regarding McCleod’s prior statement that he never heard Rosemond use the words “kill” or “murder,” as such questioning was not inconsistent with Rosemond’s proffer statement that he “knew [Fletcher] was going to be dead.” App. 204.
Finally, it is significant that at both trials it was the Government that elicited from McCleod the fact that Rosemond did not use the words “murder” or “kill.” The Government did so on its direct examination of McCleod at the first trial, and during its redirect examination of McCleod at the second trial. At minimum, the Government opened the door, and defense counsel should not have been foreclosed from following up in cross-examination, recross-examination, or summation. Because the district court’s interpretation of the scope of the waiver provision was unduly narrow, its restrictions on Rosemond’s ability to cross-examine his witnesses and mount an effective defense violated the Sixth Amendment. See Oluwanisola, 605 F.3d at 133.
D. Harmlessness
Constitutional errors of this type are subject to harmless error review. Oluwanisola, 605 F.3d at 133. In assessing harmlessness, we ask “whether we can ‘conclude with fair assurance’ that the errors ‘did not substantially influence the jury.’ ” Id. (quoting United States v. Ivezaj, 568 F.3d 88, 98 (2d Cir. 2009)). We consider “(1) the importance of ... unre-*113butted assertions to the government’s case; (2) whether the excluded material was cumulative; (3) the presence or absence of evidence corroborating or contradicting the government’s case on the factual questions at issue; (4) the extent to which the defendant was otherwise permitted to advance the defense; and (5) the overall strength of the prosecution’s case.” United States v. Gupta, 747 F.3d 111, 133-34 (2d Cir. 2014) (alteration in original) (quoting Oluwanisola, 605 F.3d at 134).
The error was not harmless. Indeed, the Government does not even argue in the alternative that it was. See Gov’t Br. 31-44. The Government did, however, make such an argument in Oluwanisola, in similar circumstances. And we rejected that argument, even though, in that case, “defense counsel was permitted to make sufficiency arguments during summation.” 605 F.3d at 134. Here, defense counsel was not permitted to make any sufficiency argument at any point during trial, whether during his opening, cross-examination, or closing. The district court’s ruling therefore “had the effect of severely limiting [Rosemond’s] ability to mount an effective defense. In a situation such as this one, where defense counsel risked letting the horse out of the barn if he did not closely adhere to the court’s ruling, this limitation was substantial.” Id.
We hold that the preclusion of defense arguments and cross-examination was not harmless error, and vacate Rosemond’s convictions and remand for a new trial.4
II. Sufficiency of the Evidence
Rosemond also argues that the Government failed to produce sufficient evidence to prove that Rosemond committed murder for hire or conspired to murder for hire because of the lack of evidence that Rosemond intended that Fletcher be killed. We reach this question despite our decision that Rosemond’s conviction should be vacated on the grounds discussed above because, “if we were to conclude that there was insufficient evidence, we would be required to direct the district court to enter a judgment of acquittal,” instead of a vaca-tur and remand for a new trial. Oluwani-sola, 605 F.3d at 134 n.4.
We review challenges to the sufficiency of evidence de novo, and will uphold a conviction if “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Vernace, 811 F.3d 609, 615 (2d Cir. 2016) (quoting Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)). In doing so, we “must view the evidence in the light most favorable to the government, crediting every inference that could have been drawn in the government’s favor, and deferring to the jury’s assessment of witness credibility and its assessment of the weight of the evidence.” United States v. Coplan, 703 F.3d 46, 62 (2d Cir. 2012) (quoting United States v. Chavez, 549 F.3d 119, 124 (2d Cir. 2008)). “A defendant bears a heavy burden in -seeking to overturn a conviction on grounds that the evidence was insufficient.” United States v. Aleskerova, 300 F.3d 286, 292 (2d Cir. 2002) (internal quotation marks omitted).
There was sufficient evidence to show that Rosemond committed a.murder for hire and conspired to do so with his associates. First, through cooperating witnesses, the Government presented a number of statements made by Rosemond *114from which an intent to murder could be inferred. For instance, witnesses testified that Rosemond said “something like they’re not going to understand what it is until they’re carrying a coffin,” App. 315, and in connection with Fletcher’s anticipated return home from prison, that “these dudes ain’t gonna be happy until they go to a funeral,” App. 266. Second, the jury could infer from the extent of planning and coordination that murder was the object of the conspiracy. Third, while Rosemond paid Czar associates $5,000-$10,000 for nonfatal attacks on other G-Unit associates, their homes, and their cars, he offered $30,000 to anyone who would bring him Fletcher. Compared to the other shootings described during the course of the trial, the Fletcher shooting involved multiple meetings, coordination, • and stealth, including the purchase of a separate phone used exclusively for communicating with Fletcher. Finally, Rosemond’s behavior following Fletcher’s death could reasonably imply that his goal had been achieved. After hearing that Fletcher had been killed, rather than become angry or express regret, Rosemond gloated to friends about what had occurred and paid the participants for their actions.
In sum, viewing the evidence in the light most favorable to the Government, we conclude there was sufficient evidence to support Rosemond’s convictions, and therefore decline to direct the District Court to enter a judgment of acquittal.5
CONCLUSION
For the reasons set forth above, we VACATE Rosemond’s convictions and REMAND to the district court for further proceedings consistent with this opinion.
. In the Eastern District of New York, Rose-mond was convicted of engaging in a continuing criminal enterprise and numerous related narcotics, firearms, and money laundering counts. He was sentenced principally to life imprisonment. See United States v. Rosemond, 595 Fed.Appx. 26 (2d Cir. 2014) (summary order) (substantially affirming convictions and sentence).
. The Government also argued that certain questions posed by defense counsel to the medical examiner about the caliber of the gun used furthered the implicit argument that Rosemond did not intend to murder Fletcher, and thus triggered Rosemond's proffer agreement waiver. The trial court found that the alleged implication of such questions—that a small-caliber gun would not be used for a murder—did not support such an argument.
. We do not foreclose the possibility that, in unusual circumstances not presented here, such cross-examination could suffice to trigger the "factual assertion” requirement of a proffer waiver.
. Because we vacate the convictions on these grounds, we do not reach Rosemond’s argument that the district court abused its discretion in admitting certain uncharged act evidence as excessive and prejudicial.
. We note that our holding that the district court’s error was not harmless but that a judgment of acquittal should not be entered is not internally inconsistent. The standards that we apply to determine whether an error was harmless and whether a judgment of acquittal should be entered are substantially different. When undertaking the latter analysis, we ask whether "any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” Vemace, 811 F.3d at 615. Just because a rational trier of fact could have found that Rosemond had the requisite intent does not mean that a rational trier of fact must have done so, or that we can "conclude with fair assurance that the [district court's] errors did not substantially influence the jury.” Oluwanisola, 605 F.3d at 133 (internal quotation marks omitted).