SUMMARY ORDER

Defendants-appellants Darrin Carathers and Darryl Adams appeal from judgments of conviction following a jury trial. Carathers and Adams were both convicted of *74distributing and possessing with intent to distribute cocaine in violation of 21 U.S.C. § 841(b)(1)(C). Adams was also convicted of conspiracy to distribute and to possess with the intent to distribute five or more grams of crack cocaine, in violation of 21 U.S.C. §§ 846 & 841(b)(1)(B), and of that underlying substantive offense, in violation of 21 U.S.C. § 841(b)(1)(B). We assume the parties’ familiarity with the facts and procedural history of the case.

Both Adams and Carathers raised the defense of entrapment at trial. Because the government conceded that the drug transactions at issue were initiated by government agents, much of the evidence and arguments at trial focused on whether the defendants were predisposed to commit the charged crimes. See United States v. Brand, 467 F.3d 179, 189 (2d Cir. 2006) (“[T]he government can ... defeat the defense of entrapment if it can show that a defendant was predisposed to commit the crime.”). On appeal, Adams (but not Carathers) claims that the trial evidence was insufficient to establish Adams’ predisposition. We disagree.

A defendant bears a heavy burden in challenging the sufficiency of evidence: we review all of the evidence “in the light most favorable to the government,” and we must sustain the jury’s verdict if “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Walker, 191 F.3d 326, 333 (2d Cir. 1999) (quotation marks and emphasis omitted). Predisposition to commit a crime may be established by evidence of: (1) an existing course of criminal conduct similar to the crime for which the defendant is charged; (2) an already formed design on the part of the accused to commit the crime for which he is charged; or (3) a willingness to commit the crime for which he is charged as evidenced by the accused’s ready response to the inducement. Brand, 467 F.3d at 191.

In this case, reasonable jurors could have found that Adams was predisposed to commit the crimes for which he was convicted. Although Adams testified that he was not involved in the drug trade prior to being approached by the government’s agent, reasonable jurors could conclude otherwise based, in part, on tape-recorded conversations in which Adams evinced a keen understanding of the narcotics trade and referred to “[his] people” selling “bricks,” i.e., kilograms, of cocaine. Moreover, based on the expediency and manner in which the transactions were completed, the jury could reasonably conclude that Adams was perfectly willing to avail himself of the government-initiated opportunity to sell both cocaine and crack. See, e.g., United States v. Salerno, 66 F.3d 544, 547 (2d Cir. 1995).

Defendants also claim that the district court erred — both procedurally and substantively — in its supplemental jury instructions in response to oral questions by the jury on the issues of entrapment and the burden of proof.2 In United States v. Ronder, 639 F.2d 931, 934 (2d Cir. 1981), we outlined a four-step procedure for responding to jury messages: (1) The jury’s *75question should be submitted in writing; (2) the question should be marked as a court exhibit and read into the record; (3) counsel should be given an opportunity to request appropriate responses; and (4) once the jurors are recalled, the question, if substantive, should be read into the record in them presence. Id. We have since recognized, however, that “some latitude in determining how best to handle jury inquiries” must be left to the district court, and have held that vacatur is not required when a judge’s responses to oral jury questioning does not prejudice the parties. See United States v. Ulloa, 882 F.2d 41, 45 (2d Cir. 1989).

As an initial matter, we need not determine whether defendants waived them procedural challenge, or whether the procedure employed by the district court was erroneous under the circumstances, because defendants fail to demonstrate any prejudice resulting from the substance of the court’s supplemental instructions. See Ulloa, 882 F.2d at 45.3 First, defendants claim that the district court’s use of the word “cajole” in the supplemental instructions concerning entrapment impermissibly operated to shift the jurors’ attention to the government actor’s conduct rather than to the defendants’ state of mind.4 However, when read in the context of the entire supplemental instructions, as well as the original jury charge, the jury was clearly instructed that the government bore the burden of proving that defendants were ready and willing to commit the drug-crimes at issue, and that the defendants’ frame of mind prior to being approached by the government agent was what the jury had to decide. See, e.g., United States v. Tillem, 906 F.2d 814, 826 (2d Cir. 1990) (explaining that we review the “legal sufficiency of supplemental instructions ... in light of the jury instructions as a whole”). The district court’s use of the word “cajole” was simply offered as a contra-example of what would not satisfy the government’s burden of overcoming the entrapment defense. We thus find no legal error or prejudice in the district court’s supplemental entrapment instructions. Cf. e.g., United States v. Hulett, 22 F.3d 779, 781 (8th Cir. 1994) (finding sufficiency of evidence that defendant was “disposed to commit the crimes for which he was convicted,” where he was “not cajoled into the transaction”).

Nor do we find any substantive error or prejudice stemming from the dis*76trict court’s supplemental instructions concerning the government’s burden of proof. In particular, Carathers objects to the district court’s supplemental instruction that the words “beyond a reasonable doubt” is “not a question of speculation or gut feeling or shrugging of one’s shoulders or anything else.” This instruction appears to have been intended as a reminder that a “doubt” based on mere conjecture is not a “reasonable doubt.” Even if the district court’s instruction might be read to suggest that the jurors be able to articulate a reason for a doubt, we have refused to find such a suggestion erroneous. See, e.g., Vargas v. Keane, 86 F.3d 1273, 1276-78 (2d Cir. 1996); United States v. Davis, 328 F.2d 864, 867-68 (2d Cir. 1964). Moreover, we find no merit to Carathers’ related claim that the district court’s use of the term “gut feeling” was intended to reference his counsel’s summation, whose opening line was “Ladies and Gentlemen, what does your gut tell you.” There is no evidence that the district court had that intent. In any event, as counsel for Carathers himself concedes, the thrust of his argument — reflected in his later statements to the jury — was to appeal to the jurors’ common sense. Nothing in the district court’s supplemental instruction, especially when considered in combination with the original instruction, impermissibly undermined counsel’s effort.

Finally, we review the district court’s denial of Adams’ motion for a new court-appointed counsel for abuse of discretion, see United States v. Simeonov, 252 F.3d 238, 241 (2d Cir. 2001), and we find none here. In general, we examine four factors in reviewing a district court’s denial of a request for new counsel: (1) whether the defendant’s motion was timely; (2) whether the trial court adequately inquired into the matter; (3) whether the conflict between the defendant and his attorney was so great that it resulted in a total lack of communication preventing an adequate defense; and (4) whether the defendant substantially and unjustifiably contributed to the breakdown in communication. See United States v. John Doe No. 1, 272 F.3d 116, 122-23 (2d Cir. 2001). Here, Adams’ request for new counsel— raised for the first time near the close of the sentencing proceeding — was not timely. Moreover, the court’s inquiry into the matter revealed no indication that communications had broken down between Adams and his counsel, and any rift in the attorney-client relationship was at least partially Adams’ fault. Under these circumstances, the district court did not abuse its discretion in denying Adams’ request for new counsel.

For the foregoing reasons, the district court’s order is AFFIRMED.