Opinion for the Court filed PER CURIAM.
Concurring opinion filed by Circuit Judge TATEL.
PER CURIAM:Convicted by a jury of committing and conspiring to commit fraud and theft from the Superior Court of the District of Columbia, appellant argues that the district court improperly allowed counsel to offer supplemental arguments in response to factual questions that the jury asked after *1314commencing its deliberations. He also contends that the district court erred by refusing to declare a mistrial when a juror reported having had a brief contact with the government’s star witness. Addressing only the first of these arguments, we conclude that the district court abused its discretion by permitting the supplemental arguments, and we therefore reverse the conviction and remand for a new trial.
I.
Appellant Shola Ayeni, an attorney, served as appointed counsel for criminal defendants in the Superior Court of the District of Columbia. In 2002, a grand jury indicted him and one of his investigators, Troy Robinson, on charges of committing and conspiring to commit fraud and theft from programs receiving federal funds. According to the indictment, Ayeni and Robinson ran a scheme whereby Ayeni obtained nearly 2,000 of the vouchers that attorneys representing poor criminal defendants in the Superior Court provide to people required to testify in their clients’ cases. Ayeni then gave the vouchers, each worth $40, to Robinson, who had friends and family members' — not one of whom was a witness — redeem them and give the money (minus a commission) to him. He in turn gave the money to Ayeni. Robinson received nothing during these transactions; Ayeni allegedly promised to give him thousands of dollars worth of other vouchers later.
Ayeni’s first trial ended in a hung jury. Before the re-trial, the government secured Robinson’s testimony detailing his scheme with Ayeni, testimony it presented along with that of six people who cashed vouchers for Ayeni and Robinson, several Superior Court employees who issued vouchers to Ayeni, and a handwriting expert who compared signatures on the vouchers with Robinson’s and Ayeni’s signatures. The government also introduced evidence indicating that Ayeni experienced financial problems at the time he allegedly ran his scheme. Ayeni adduced no evidence.
A few hours after the jury began deliberating, it sent a note to the court stating that it was “hopelessly deadlocked.” Denying Ayeni’s motion for a mistrial, the court invited, but did not require, the jurors to identify areas of disagreement, stating that perhaps it or counsel could help them resolve those disagreements. The jury retired and soon sent in three questions: “What is the lesser count Mr. Ayeni is charged with; why was the handwriting expert called to testify; do[] the defense and prosecution agree that Mr. Ayeni’s signatures in the witness voucher record books are authentic?” Tr. 12/13/02 at 10, reprinted in J.A. at 158. With the two sides’ consent, the court responded to the first question by informing the jurors that there were no lesser included offenses. That response is not at issue in this appeal.
As to the second and third questions, the court told counsel that it was inclined to give each side time to present supplemental arguments, partly because it felt it could not provide the jury with a fair and adequate response. Ayeni objected to the arguments and again moved for a mistrial, but after giving each side a day to research the issue and submit a memorandum, the court stood by its initial plan and permitted each lawyer up to ten minutes to argue, with defense counsel going first. Both before and after the attorneys argued, the district court instructed the jury not to “place undue emphasis on these supplemental arguments,” Tr. 12/16/02 at 7, 18, reprinted in J.A. at 181, 192, but to consider them together with the evidence, instructions, and other arguments they had heard.
*1315Shortly after the supplemental arguments, the jury sent another note, this one stating that one juror had had a brief contact with Robinson six days earlier, not long after Robinson testified, and that the juror had shared the encounter with the other jurors. During the encounter, which occurred in a courthouse elevator, Robinson asked the juror, “[d]o you know where I can get any vouchers around here?” to which the juror responded: “I don’t know anything about any — I’m new around here. I don’t know what you are talking about.” Id. at 27, reprinted in J.A. at 201. In response to the jury’s note, the court interviewed the jurors separately, asking whether they could ignore whatever they had heard about the contact and decide the case based solely on the evidence presented. When all said they could, the judge denied Ayeni’s motion for a mistrial and allowed the jurors to resume deliberations. A few hours later, the jury convicted Ayeni on all counts. The district court subsequently denied his motion for a new trial. See United States v. Ayeni, 245 F.Supp.2d 145, 150 (D.D.C.2003).
On appeal, Ayeni contends that the district court erred both in allowing the supplemental arguments and in refusing to grant a mistrial based on Robinson’s contact with the juror. Because we agree with the first contention, we do not address the second.
II.
In asserting that the district court improperly allowed supplemental arguments, Ayeni makes two alternative arguments. First, he contends that supplemental arguments in response to deliberating juries’ factual questions are never permitted because they “subvert[ ] the principle ... that the jury’s deliberations must remain inviolate,” Appellant’s Br. at 11, and “intrude[] upon the jury’s exclusive role as the factfinder,” Appellant’s Reply Br. at 3. Second, he claims that even if such supplemental arguments are sometimes permissible, in this case the district court abused its discretion by allowing them. Although the government acknowledges that the second, narrower argument is properly before us, it insists that Ayeni forfeited the first, broader argument by failing to make it in the district court.
We need not resolve the government’s forfeiture argument because we agree with Ayeni that the district court abused its discretion by allowing supplemental arguments in this case. Ayeni makes several points in advancing his narrower argument, but we begin and end with the one we deem most important: that the jury’s questions necessitated no additional argument. In his opinion denying Ayeni’s motion for a new trial, the district judge explained his decision to allow the supplemental arguments:
I could have attempted to fashion an answer that characterized the government’s position concerning the importance of the handwriting expert’s testimony, and the parties’ positions about the questioned signatures. The risk was that such an instruction from the Court, worded so as to avoid lapsing into advocacy, might not sufficiently or fairly capture the parties’ nuanced positions and would be unresponsive. Alternatively, I could have simply instructed the jurors that they had to rely upon their recollection of the evidence and arguments. That would have been of no help. Helpful and responsive answers required advocacy.
Ayeni 245 F.Supp.2d at 149. Challenging this reasoning, Ayeni asserts — and the government agrees — that the jury’s inquiry as to whether the two sides agreed that certain signatures were authentic could have been adequately answered with one *1316word: “.no.” As to the question about why the government called the handwriting expert, Ayeni argues that “the district court could have collaborated with [the] attorneys to formulate a neutral ... response ... such as ‘The handwriting expert was called to testify because the Government and the defendant dispute the authenticity of the signatures on the witness vouchers.’ ” Appellant’s Reply Br. at 11. The government counters that answering this question “required a partisan slant on the evidence that the judge could not properly provide.” Appellee’s Br. at 27.
We agree with Ayeni that supplemental arguments were an inappropriate response to the jury’s questions. The question about whether the parties agreed on the signatures’ authenticity was straightforward, and the one-word answer that both sides suggest here would have provided a direct and complete response. The other question, which sought information about the government’s trial strategy, similarly called for no supplemental arguments, for the district court could have fashioned a response along the lines Ayeni suggests, or it could have told the jurors that the question was not one it could answer because trial strategy was not a proper concern of theirs. In fact, the court took just such an approach when it answered the jury’s question about lesser-included offenses, telling the jurors that if they were asking which of the charges involved a shorter sentence, the court could not respond substantively because “[t]he question of possible punishment of the defendant in the event of conviction is ... no concern of yours and should not enter or influence your deliberations in any way.” Tr. 12/16/02 at 6, reprinted in J.A. at 180. Given these other options, it was an abuse of discretion for the district court to adopt an approach that, in effect, allowed the lawyers to hear the jury’s concerns and then, as if they were sitting in the jury room themselves, fashion responses targeted precisely to those concerns. Indeed, in his supplemental argument the prosecutor made one argument to the jury that he had not made in his closing: that there was a reason why the handwriting expert had been unable to say for certain that any of the signatures on the vouchers or in the voucher sign-out book were Aye-ni’s, namely that the signatures were sometimes made in an automobile. The prosecutor offered this reason even though the expert herself never gave it as an explanation for her inability to match any signatures.
It is true, as the government says, that a “district court enjoys broad discretion in controlling the jury during deliberations,” Appellee’s Br. at 23, and that “[t]his discretion includes the authority to decide what to do when the jury encounters stumbling blocks in its deliberations,” id. at 24. Yet this discretion has limits. For example, district courts may not ask a deliberating jury how it is numerically divided, see Brasfield v. United States, 272 U.S. 448, 449-50, 47 S.Ct. 135, 136, 71 L.Ed. 345 (1926), nor (at least in this circuit) give the so-called “dynamite” or Allen charge used to break deadlocks, see United States v. Thomas, 449 F.2d 1177, 1186 (D.C.Cir.1971) (en banc). The issue, then, is not whether district courts have the discretion the government describes — they unquestionably do — but whether the court’s action here fell within the scope of that discretion. For the reasons already discussed, we conclude that it did not.
As mentioned, Ayeni argues not only that the supplemental arguments were an abuse of discretion in this case, but also that such arguments are never permissible because they invade the jury’s deliberations and intrude into its role as the sole trier of fact. Though we need not *1317address this contention given our resolution of Ayeni’s narrower claim that the supplemental arguments were an abuse of discretion under the circumstances of this case, we note our uneasiness with any use of supplemental arguments in response to a jury’s factual questions. In addition to being almost unheard of — the parties cite but one case in which they were employed — the use of such arguments is, for the reasons Ayeni suggests, troubling. Accordingly, we strongly discourage the use of this innovation by the trial judges of this circuit.
Of course, the district court’s error in allowing supplemental arguments would not require us to vacate Ayeni’s conviction had that error been harmless. See Fed. R.Crim.P. 52(a) (“Any error, defect, irregularity, or variance that does not affect substantial rights must be disregarded.”). But the government bears the burden of proving harmless error, see, e.g., United States v. Whitmore, 359 F.3d 609, 622 (D.C.Cir.2004) (citing United States v. Olano, 507 U.S. 725, 734, 113 S.Ct. 1770, 1777, 123 L.Ed.2d 508 (1993)), and here it does not even venture to make a harmless error argument. This is unsurprising, since there is no way to know whether the supplemental arguments produced the jury’s verdict. We thus reverse Ayeni’s conviction and remand for a new trial.
So ordered.