BORK, Circuit Judge:

This case arises out of a fraudulent scheme involving mortgage loans that caused many borrowers to lose their homes and to incur ruinous debts. The defendants who appeal their convictions — Augustine F. Barquin, Roland T. Butler, Charles E.L. Clay, Norman C. Tillette, and C. Jimmie Vaccaro — were all associated with the Nationwide Mortgage Company of Falls Church, Virginia. Tillette was the owner and president of the company, Vaccaro acted as the settlement attorney on many of the loans, and Barquin, Butler, and Clay were brokers who solicited customers to obtain mortgage loans from the company.

Nationwide solicited homeowners to borrow money, and, in order to evade the usury laws, got the borrowers to state that the loans were for business purposes, though typically the loans had nothing to do with businesses of any kind. The brokers induced borrowers to sign one-year, interest-only notes that required large back-end payments to be made at the end of the year. The most significant inducements were frequent promises that refinancing would be made available, though typically it was not. On the contrary, borrowers who sought help or advice on their loans usually found that the loan brokers had become very elusive and were difficult if not impossible to reach either at the company or at home. By these and other means, Nationwide ended up charging borrowers an interest rate that was three or four times larger than the 15% limit that the local usury laws prescribed during this period.

These five defendants were charged with conspiracy to violate the Truth in Lending Act, see 15 U.S.C. § 1611 (1982); 18 U.S.C. § 371 (1982), and with various charges of violating, conspiring to violate, or aiding and abetting violations of the Travel Act, see 18 U.S.C. § 2314 (1982), by transporting individuals in interstate commerce in furtherance of a scheme to defraud. A jury convicted each defendant on the charges under the Truth in Lending Act and on several of the charges under the Travel Act. Defendants raise several claims of error on appeal. We affirm the convictions.

Two of the defendants advance procedural objections. Butler argues that the district court erred in refusing to grant his motion for a bill of particulars. Under the Federal Rules of Criminal Procedure, a court “may direct the filing of a bill of particulars.” Fed.R.Crim.P. 7(f). A bill of particulars can be used to ensure that the charges brought against a defendant are stated with enough precision to allow the defendant to understand the charges, to prepare a defense, and perhaps also to be protected against retrial on the same charges. See, e.g., United States v. Gorel, 622 F.2d 100, 104 (5th Cir.1979), cert. denied, 445 U.S. 943, 100 S.Ct. 1340, 63 L.Ed.2d 777 (1980). Yet if the indictment is sufficiently specific, or if the requested information is available in some other form, then a bill of particulars is not required.

Butler sought a bill to require the government to state the approximate times and the places at which Butler entered and exited the alleged conspiracy. The indictment did not contain this information, though it did recount the dates of a number of overt acts by which it is alleged that Butler participated in the conspiracy. See Indictment at 10-11. In its response to the motion for a bill of particulars, moreover, the government stated that Butler made loans for Nationwide between March, 1981, and February, 1982, and continued his employment with Nationwide until the end of 1982. See Government’s Response to De*132fendant Butler’s Motion for Bill of Particulars at 2. Since the alleged conspiracy revolved around the making of these loans, this response furnished essentially the information that Butler had requested. More specific information about the times and places that Butler participated in the alleged conspiracy was not required by law. See, e.g., United States v. Pollack, 534 F.2d 964, 970 (D.C.Cir.), cert. denied, 429 U.S. 924, 97 S.Ct. 324, 50 L.Ed.2d 292 (1976). In any event, the determination of whether a bill of particulars is necessary rests within the sound discretion of the trial court, see id., and we cannot say that the district court abused its discretion here.

Barquin contends that the district court erred by failing to grant his motion for severance. All the defendants in this case were tried jointly, and Barquin claims that he should have been tried separately because the evidence against the other defendants was “far more damaging” than the evidence against him. United States v. Sampol, 636 F.2d 621, 645 (D.C.Cir.1980).

Barquin’s contention has no merit. The trial judge is given great latitude to balance the institutional benefits that joint trials confer by preserving judicial and prosecutorial resources against the possibility that a defendant will be erroneously convicted because the cumulation of the evidence against all the defendants may lead the jury to be either confused or prejudiced in assessing the evidence against that particular defendant. See, e.g., United States v. Hines, 455 F.2d 1317, 1334 (D.C.Cir.), cert. denied, 406 U.S. 975, 92 S.Ct. 2427, 32 L.Ed.2d 675 (1972). Instructions to the jury to consider the evidence separately against each defendant, such as were given in this case, provide significant safeguards against the dangers of prejudice. See United States v. Slade, 627 F.2d 293, 309 (D.C.Cir.), cert. denied, 449 U.S. 1034, 101 S.Ct. 608, 66 L.Ed.2d 495 (1980). Barquin’s claim that a great disparity existed between the evidence against him and the evidence against the other defendants is untrue. He notes that he was named in only 4 of the 17 counts and in only 8 of the 49 overt acts alleged to be in furtherance of the conspiracy. These numbers seem to represent small fractions only because several defendants were charged together in the indictment. In fact, the numbers demonstrate no less involvement by Barquin than by any of the other brokers charged in the indictment. Both Tillette and Vaccaro were charged with more counts simply because their roles in the conspiracy were somewhat broader than those played by the individual loan brokers. Barquin’s contention falls well short of demonstrating any abuse of discretion by the district court.1

II.

The next claim of error, and the only one joined by all the defendants on appeal, presents a more difficult issue. On the fifth day of the trial, one of the jurors told a deputy marshal that she had a contact with one of the defendants in the courthouse elevator. The juror stated that the defendant, Tillette, approached her and told her that she was a wonderful lady, that he had met a lot of people whom he had tried to help by giving them a check, and that those people had now come to court as witnesses and were causing him trouble. Tr. at 898-99. The juror apparently said nothing and walked away. Tillette denied that any such conversation had occurred.

When the trial judge was informed of the improper contact, he immediately called the juror in and interviewed her in the presence *133of counsel. The judge had the juror describe the encounter, then asked her if it would have any bearing on her ability to serve as a juror and to render a fair and impartial verdict. She replied that it would not. He also cautioned her not to discuss the matter with the other jurors. She assured the judge that she would not do so. She was then dismissed. The judge did not ask her if she had already mentioned the matter to the other jurors. After the juror had returned to the jury room, one of the counsel asked whether she might have already talked to the other jurors about the improper contact. The deputy marshal, however, firmly stated that she had not done so. The judge then questioned Tillette and another defendant about the matter. See Tr. at 896-903.

Later in the trial, the government’s counsel raised the matter again, asking that the juror be excused. The judge considered recalling the juror for further questioning about whether she had discussed the improper contact with the other jurors, but decided not to do so after reiterating the deputy marshal’s representation and voicing concern that another interview might only cause the juror to magnify the significance of the contact beyond its true importance. He also decided not to dismiss the juror at that point, which would have required him to use up one of the four available alternates, but invited counsel to renew their request to dismiss the juror after the entire case had been presented. See Tr. at 944-49. None of the counsel renewed the request, and the juror participated in the jury’s deliberations.

The day after the jury returned guilty verdicts against these defendants, the court learned that the juror had in fact discussed the improper contact with others on the jury. The judge promptly reassembled the entire jury, with the exception of the juror to whom Tillette had spoken and who had been questioned previously. The judge interviewed the jurors individually, in the presence of all opposing counsel, asking whether each one knew of the improper contact, what was known about the contact, and whether this knowledge had any effect on the juror’s ability to reach a fair and impartial verdict.

In his questioning of the eleven jurors, the judge discovered that one did not know of the contact, seven knew of the contact but did not know what was said, and three knew at least part of what the defendant is alleged to have said. All the jurors stated that the matter had no effect on their ability to render a fair and impartial verdict. See Post-Trial Hearing Tr. at 26-40. The judge refused to recall the juror previously interviewed, and refused to ask several more detailed questions suggested by counsel. See id. at 5-24, 42-43. The judge later denied defendants’ motion for a new trial, finding that “the nature of the communication by defendant Tillette was not of the type which is inherently prejudicial and that knowledge of the communication by some members of the jury had no effect on their deliberations or verdicts, and that such communication was harmless.” United States v. Tillette, Crim. No. 85-404 (D.D.C. Apr. 23, 1986) (order denying oral motion for new trial).

The proper legal standard for evaluating the effect of an alleged juror exposure to extra-judicial information, both sides here seem to agree, is that “[irrespective of the source of the alleged taint, it is the burden of the government to demonstrate that the jury was impartial, and that extrinsic information did not contribute to the verdict.” Brief for Appellee at 12.2 As *134Remmer v. United States, 347 U.S. 227, 74 S.Ct. 450, 98 L.Ed. 654 (1954), and Smith v. Phillips, 455 U.S. 209, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982), state, the proper procedure for the judge confronted with an allegedly improper juror contact is to hold a hearing “to determine the effect of such occurrences when they happen.” Phillips, 455 U.S. at 217, 102 S.Ct. at 946. The hearing should not be conducted ex parte, see, e.g., Remmer, 347 U.S. at 229-30, 74 S.Ct. at 451, but it also need not be conducted as a full evidentiary hearing, see, e.g., Phillips, 455 U.S. at 216-18, 102 S.Ct. at 945-46; United States v. Boscia, 573 F.2d 827, 831 (3d Cir.1978), and the inquiries put to the juror need only be sufficiently detailed to permit the judge to determine whether any prejudice is likely to result. See, e.g., United States v. Coleman, 805 F.2d 474, 481-82 (3d Cir.1986); United States v. Pennell, 737 F.2d 521, 529, 533 (6th Cir.1984), cert. denied, 469 U.S. 1158, 105 S.Ct. 906, 83 L.Ed.2d 921 (1985). In these and other aspects of this problem the trial judge has broad discretion to fix the exact procedures by balancing the need to make a sufficient inquiry against the concern that the inquiry not create prejudicial effects by unduly magnifying the importance of an insignificant occurrence. See, e.g., United States v. Polizzi, 500 F.2d 856, 880-81 (9th Cir. 1974), cert. denied, 419 U.S. 1120, 95 S.Ct. 802, 42 L.Ed.2d 820 (1975); United States v. Webster, 750 F.2d 307, 338 (5th Cir.1984), cert. denied, 471 U.S. 1106, 105 S.Ct. 2340, 85 L.Ed.2d 855 (1985). The judge then determines whether the exposure was prejudicial or harmless, and appellate courts must defer to this finding on review. See, e.g., Hobson v. Wilson, 737 F.2d 1, 49 (D.C. Cir.1984), cert. denied, 470 U.S. 1084, 105 S.Ct. 1843, 85 L.Ed.2d 142 (1985); Irvin v. Dowd, 366 U.S. 717, 723, 81 S.Ct. 1639, 1643, 6 L.Ed.2d 751 (1961). The burden of establishing harmlessness, which is placed on the government, is made less demanding by the trial judge’s participation and use of all the tools necessary to evaluate the relevant facts.

In this instance we are unable to find error in the trial court’s conclusion that the juror contact was harmless. When informed of the contact, the judge immediately convened a hearing in the presence of opposing counsel, all of whom were given a chance to make suggestions on how to proceed. The affected juror was brought into the hearing and extensively questioned. The judge’s questioning fully revealed the details of the alleged exchange between the defendant and the juror. The nature of the contact was relatively innocuous; it did not provide the juror with any crucial extra-judicial information, and it did not constitute an attempt to bribe or intimidate the juror, which is the kind of contact that clearly could, in and of itself, prejudice the juror. Cf. United States v. Delaney, 732 F.2d 639, 641 (8th Cir.1984) (extra-judicial information); Owen v. Duckworth, 727 F.2d 643, 644 (7th Cir.1984) (threat). The judge specifically asked the juror if the contact would have any bearing on her ability to render a fair and impartial verdict, and she stated that it would not. Although some courts have doubted the reliability of juror responses to this kind of question, the Supreme Court *135has settled that such testimony is not “inherently suspect,” for a juror “ ‘is well qualified to say whether he has an unbiased mind in a certain matter.’ ” Phillips, 455 U.S. at 217 n. 7, 102 S.Ct. at 946 n. 7 (quoting Dennis v. United States, 339 U.S. 162, 171, 70 S.Ct. 519, 523, 94 L.Ed. 734 (1950)). These facts fully justify the trial judge’s ruling that the contact was harmless.

The principal shortcoming of the trial judge’s handling of the matter was his failure to determine at the hearing whether the juror had discussed the incident with anyone else on the jury. The judge admonished her not to mention it to the other jurors; it would have been a simple matter for him merely to ask her if she had done so already. The omission of this question later resulted in additional problems and necessitated the reassembling of all the other jurors at a post-trial hearing. That was regrettable. We understand that the matter may be clearer in hindsight and also that the judge may have thought himself entitled to rely on the representations made by the deputy marshal, but it would be better practice to put all relevant questions directly to the juror.

We believe, nevertheless, that the inquiries made at the post-trial hearing were adequate to support the trial court’s conclusion that any discussion of the contact among the jurors did not prejudice the defendants. Again, the judge’s inquiries uncovered what each juror knew of the contact, and ascertained that this knowledge did not render any juror unable to return a fair and impartial verdict. Even though this testimony* came after trial, thus raising some concern about whether the jurors might be reluctant to impeach their own verdict, the judge was entitled to rely on their testimony if he found it credible. See Phillips, 455 U.S. at 217 n. 7, 102 S.Ct. at 946 n. 7. Nor did the judge err in failing to recall the contacted juror. Although that might have been better practice, since the testimony of the other jurors might have made her testimony useful, we accept as reasonable the judge’s explanation that his earlier questioning of the juror had established that she was not prejudiced by the contact. We think we cannot overturn the district court’s finding that there was no prejudice to the defendants. That court correctly denied the motion for a new trial.

III.

Two other claims raised need be addressed only briefly. Butler claims that the trial judge erred by denying a suggested jury instruction that good faith is a defense to charges involving fraud or conspiracy to defraud. The judge found that the record did not provide sufficient foundation to require the requested instruction. We agree. The defense of good faith to charges of fraud rests essentially on the representation that a plan or scheme seemed practical or at least plausible to its proponents ex ante even though it later produced a financial disaster. An instruction on good faith cautions the jury against finding fraud by evaluating what originally may have been a passable business judgment solely in light of an ex post evaluation of the plan’s ultimate failure. See, e.g., Steiger v. United States, 373 F.2d 133, 136 (10th Cir.1967).

This case, however, does not turn simply on assessing the practicality of a business scheme. Here there was substantial testimony that Butler regularly attended the brokers’ meetings and discussions about the scheme, and that he encouraged potential borrowers to state that the loans they sought were for business purposes when he knew the loans would not be used for business purposes. In addition, there was evidence that Butler aided borrowers in inventing figures to support claims of business purpose. His participation in and comprehension of the scheme may not have been as thorough as that of Tillette, but there was not enough evidence in Butler’s favor to require an instruction on a good faith defense.3 Thus, we find the jury in*136structions here, which stressed that the government was required to prove that defendants acted with specific intent to defraud others, were adequate without an additional instruction on the good faith defense. See United States v. Gambler, 662 F.2d 834, 837 (D.C.Cir.1981).

Finally, Barquin argues that there was insufficient evidence to permit the jury to find that he possessed the necessary intent to convict him of the conspiracy and Travel Act charges. But there was testimony that Barquin pressured borrowers to take out larger loans than they wanted, that he gave instructions that fictitious business purposes be stated for loans, and that he ruined borrowers in part through baseless assurances that long-term refinancing would be forthcoming. Based on this evidence, it is entirely plausible that “reasonable persons could,” as the jury here did, “find guilt beyond a reasonable doubt.” Crawford v. United States, 375 F.2d 332, 334 (D.C.Cir.1967) (emphasis in original). The convictions are

Affirmed.

. This court’s decision in United States v. Mardian, 546 F.2d 973 (D.C.Cir. 1976), which is given prominent place in Barquin's argument, is very different from this case. In Mardian, we reversed the conviction, finding that joinder of that particular defendant was unduly prejudicial. There the defendant was charged only on one count of conspiracy, unlike all his co-defendants, who were also charged with substantive crimes. In addition, the amount of evidence linking the complaining defendant to the conspiracy was much more meager than that presented against all other defendants. Neither of these factors applies to Barquin, whose position here is essentially no different from that of Butler and Clay, the other loan brokers who were convicted by the jury.

. This traditional approach was laid down in Remmer v. United States, 347 U.S. 227, 229, 74 S.Ct. 450, 451, 98 L.Ed. 654 (1954). In United States v. Pennell, 737 F.2d 521, 532 (6th Cir. 1984), cert, denied, 469 U.S. 1158, 105 S.Ct. 906, 83 L.Ed.2d 921 (1985), the Sixth Circuit held that the Supreme Court's subsequent opinion in Smith v. Phillips, 455 U.S. 209, 102 S.Ct. 940, 71 L.Ed.2d 78 (1982), reinterpreted Remmer so as to shift the burden of showing prejudice to the defendant. No other federal appellate court, however, has departed from Remmer’s statement of the legal standard for evaluating the effect of an improper judicial contact. See, e.g., United States v. Littlefield, 752 F.2d 1429, 1431-32 (9th Cir.1985) (criticizing Pennell); Owen v. Duckworth, 727 F.2d 643, 646 (7th Cir.1984); United States v. Webster, 750 F.2d 307, 338 (5th *134Cir.1984), cert. denied, 471 U.S. 1106, 105 S.Ct. 2340-41, 85 L.Ed.2d 855-56 (1985); United States v. Delaney, 732 F.2d 639, 642 (8th Cir. 1984); United States v. Hines, 696 F.2d 722, 730-31 (10th Cir.1982); Hobson v. Wilson, 737 F.2d 1, 47-49 (D.C.Cir.1984) (civil case), cert. denied, 470 U.S. 1084, 105 S.Ct. 1843, 85 L.Ed.2d 142 (1985); Haley v. Blue Ridge Transfer Co., 802 F.2d 1532, 1535 & n. 5 (4th Cir.1986) (civil case) (distinguishing Phillips). We think that Remmer’s allocation of the burden remains the law. Since the government has not contended otherwise, we need not extend this opinion with our reasons. And because we uphold the district court’s determination that none of the defendants here has been prejudiced, infra pp. 1196-1197, we need not consider whether the burden of proof on the question of prejudice should shift from the government to Tillette because he, unlike the other defendants, actually initiated the improper juror contact. That might be a correct result because, as the Seventh Circuit has said, ”[o]ur system of justice has not delegated to every reprobate the power to effect a mistrial.” United States v. Williams, 737 F.2d 594, 612 (7th Cir.1984), cert. denied, 470 U.S. 1003, 105 S.Ct. 1354, 84 L.Ed.2d 377 (1985).

. Butler suggests that his belief in the good faith of the loan scheme as a business venture is demonstrated by the fact that he also took out some loans, and eventually was himself forced *136into bankruptcy. It appears, however, that these loans did not involve falsifying business purposes, and we do not otherwise see how this fact leads to the desired conclusion that the refusal to give the requested instruction was error.