EASTERBROOK, Circuit Judge.

Evangel Capital held itself out as a lender with $250 million in assets available to churches and other religious institutions. It issued firm-commitment financing letters for multi-million-dollar projects but never closed a single loan and, indeed, never had more than $10,000 in its bank accounts. What money it did have came from fees charged to potential borrowers. Jamal Lawson, Sr., its owner and principal manager, told clients that the fees would be used to pay for appraisals and required documents; instead the fees were swiftly withdrawn and used for personal expenses. Lawson collected some $270,000 in fees and, despite his promises, did not return a penny to clients when their loans went unfunded. A jury convicted Lawson of wire fraud, 18 U.S.C. § 1343, and he has been sentenced to 52 months' imprisonment.

Lawson does not contest the sufficiency of the evidence. He told clients that he had a track record of financing religious projects; actually he never financed a single one. Essentially everything he said to the clients was false, and in a statement to federal investigators Lawson admitted diverting fees to his own use. Unfortunately, the prosecutor tried to "strengthen" an airtight case by asking the district court's approval of a plan to show that Lawson had not reported the fees as income. (Lawson had not filed tax returns at all.) The judge told the prosecutor that he could show that Lawson failed to report his income, but not that he failed to file tax returns. The prosecutor followed these instructions at trial. The judge told the jury that the evidence was admitted for the purpose of showing whether Lawson acted with knowledge or fraudulent intent — but not how it illuminated those issues, creating a needless risk that the jury used it for the forbidden purpose of treating Lawson as having a propensity to commit crimes.

The only issue raised in Lawson's appellate brief is whether the district court should have excluded the tax evidence. The United States contends that the evidence was relevant and admissible, despite Fed.R.Evid. 404(b), because it was not used to show Lawson's propensity to commit crimes. It was used, rather, to negate his contention that he intended to extend loans and failed to do so only because the state of the economy made it impossible to get financial commitments. Tax evidence could in principle undermine such a contention: if Lawson did not report the advances as business income and take deductions for the expenses of running the business, that implies that there was no legitimate business (and no legitimate business expenses). The prosecutor also maintains that a jury could understand non-reporting of the income as Lawson's implicit acknowledgment that it was the fruit of a fraud rather than a legitimate venture. Yet the prosecutor did not ask the jury to draw these inferences (or any other) when the evidence was admitted, and all the instructions said about the subject was:

This does not tell the jury how it could make proper use of the evidence. Legalese such as "knowingly and with fraudulent intent" is useless to lay jurors without concrete advice about what sort of inferences are proper or improper.

That's not the only problem with this evidence. Although Rule 404(b) says that other-act evidence may be admitted to show knowledge or intent, Rule 403 provides for exclusion of evidence when its potential for unwarranted prejudice exceeds its potential for appropriate use. United States v. Gomez, 763 F.3d 845 (7th Cir.2014) (en banc), stresses that a district judge must apply both Rule 403 and Rule 404(b) with care and exclude evidence that either lacks a proper use (Rule 404(b)) or poses excessive risk that the jury will draw the forbidden propensity inference rather than an allowable one. Rule 403 calls for a careful exercise of discretion by the district judge. See, e.g., Gomez, 763 F.3d at 856-60; United States v. Beasley, 809 F.2d 1273 (7th Cir.1987). But we can't tell whether the district judge did that, because he conducted the critical conference off the record. Back in open court, the judge put on the record what he had ruled (he would allow evidence that Lawson failed to report income but not evidence that Lawson failed to file tax returns), but not why he reached these conclusions or how he thought a jury could make proper use of the tax evidence.

If Lawson had protested at the time, he might have a solid position on appeal. District judges must think carefully and have good reasons for their dispositions under Rule 403. Silence does not suffice. But the district judge stated (on the record) that the earlier proceedings had been conducted off the record by mutual consent; Lawson does not contend otherwise. And when the judge put his rulings on the record, Lawson did not ask him to relate his reasons. There can therefore be no contention that the judge violated the Court Reporters Act, 28 U.S.C. § 753(b), or the holdings of decisions such as United States v. Nolan, 910 F.2d 1553, 1559 (7th Cir.1990), that, when judges hold conferences or discussions off the record, they must eventually record both what they concluded and why.

Nolan concerns sidebar conferences, but its approach is equally applicable to other off-the-record decisions. Our conclusion in United States v. Murphy, 768 F.2d 1518, 1535 (7th Cir.1985), that conferences held in chambers need not be transcribed does not suggest that it is sound practice for a judge to keep his reasoning entirely off the record or that an unexplained application of Rule 403 can be sustained. But Lawson's failure to ask that an adequate record be made in the district court disables him from arguing on appeal that the judge failed to conduct a proper Rule 403 analysis. For all we can tell, the judge did everything necessary — except put his thinking in the record.

Nor can Lawson protest the judge's failure to give a limiting instruction crafted to help the jury understand what sorts of inferences were appropriate and what inferences were forbidden. Although Gomez discusses the importance of situation-specific, non-boilerplate instructions — see 763 F.3d at 860-61; see also id. at 865 (opinion dissenting in part) — it also concludes that the choice whether to give a limiting instruction rests with the defense, which may decide that the less said about the evidence the better. See Gomez, 763 F.3d at 860; see also Fed.R.Evid. 105 (providing that the court must explain the use and limits of the evidence "on timely request"). Lawson did not ask the district court to give a better limiting instruction and therefore has not preserved this subject for appeal.

Still, the performance of the district judge is disappointing. We would have expected him to ensure that the record reflects his thinking and to suggest a useful instruction even if the parties failed to prompt him. The prosecutor's performance also is disappointing. Introducing evidence that stretches or exceeds the limits of admissibility in a bulletproof prosecution has nothing to recommend it, whether or not the harmless error doctrine will save the conviction; district judges can and should protect defendants and the public interest from excessive zeal by excluding such evidence.

The prosecutor's oral argument in this court was disappointing for a different reason: counsel for the United States insisted that Gomez is irrelevant because it concerns only Rule 404(b), while this appeal concerns Rule 403. That isn't remotely correct. Gomez covers the entire process of using other-act evidence, and that process has four components: whether the evidence is relevant (Rules 401 and 402); whether it is categorically inadmissible under Rule 404(b); whether if not foreclosed by Rule 404(b) it should be excluded under Rule 403; and finally, if the evidence is admissible, how the judge informs the jury about permissible and forbidden inferences. These are linked subjects. Prosecutors who do not understand and apply the full scope of the Gomez decision will find their convictions hard to sustain on appeal.

As for this appeal, however: We've already stressed that Lawson's best potential arguments are not presented for decision, and now we add that any error was harmless. The tax evidence could not have affected a rational jury's verdict, given the undisputed proof that Lawson converted the fees to his personal use and did not spend the money for the purposes he told clients it was needed. His lawyer's argument that hard times upset well-intentioned plans was embarrassed by the fact that Lawson lied when telling clients that he already had funding in hand. That he also lied about the firm's past success in securing financing, and reneged on his promises to return fees if loans did not close, cemented the prosecution's case.

AFFIRMED.