LUMBARD, Circuit Judge:
John Dioguardi and Louis Ostrer appeal from judgments of conviction entered on April 12, 1973, after a three-week jury trial held in January 1973 in the Southern District, and from the denial by Chief Judge Edelstein of new trial motions. The forty-count indictment was filed May 27, 1971, against the appellants and seven others.1 Count one charged the defendants with conspiring, in violation of 18 U.S.C. § 371 to violate provisions of the federal securities laws and regulations, 15 U.S.C. §§ 77q(a), 77x, 78j(b), and 78ff, and Rule 10b-5, 17 CFR 240.-10b-5,2 and the federal mail and wire fraud statutes, 18 U.S.C. §§ 1341 and 1343. The remaining counts charged substantive violations of these same provisions, except 18 U.S.C. § 1343.
On January 26, 1973, the jury found Ostrer guilty on eleven of the seventeen counts submitted to them by the court, and Dioguardi on four of the nineteen counts submitted as to him.3 Prior to [73]*73sentencing, the defendants moved for a new trial or, in the alternative, for an evidentiary hearing. The. basis for this motion was an unsolicited letter from one of the jurors to Dioguardi which allegedly established the ineompetency of that juror. In reliance on this, and on. the provisions of 28 U.S.C. § 1865 (b)(4), they claim that they had been deprived of their right to have their ease heard and decided by a panel of twelve competent jurors. Judge Edel-stein denied the motion on April 12th. He sentenced Dioguardi to nine years’ imprisonment and a $30,000 fine, and Ostrer to three years’ imprisonment and a $55,000 fine.4
In addition to their objections relating to alleged juror incompetency, the defendants raise four other claims of error in the conduct of the trial: first, that the government prosecutor’s argument in summation, to the effect that neither defendant called witnesses to contradict the government’s testimony, was improper comment on each appellant’s failure to testify in view of the assertion by each that he alone was in a position to contradict the government’s witnesses; secondly, that it was error for the trial court to have refused to charge, as requested, that the testimony of admitted perjurers and felons was to be scrutinized with care and caution; thirdly, that it was improper for the trial court to have ruled that Dioguar-di’s acquittal of another crime could not be proved when the government intended to utilize the acts underlying the acquittal to show a prior course of illegal conduct; finally, that consecutive sentences for Dioguardi on two of the counts charging securities law violations, counts 16 and 17, were improper since the underlying facts constituted only a single offense.
We find the defendants’ arguments unpersuasive and we accordingly affirm the convictions below and let Dioguardi’s sentences stand.
I.
The evidence at trial revealed a scheme to manipulate the price of the stock of Belmont Franchising Corporation (“Belmont"), a substantially worthless over-the-counter security. The book value of the stock was almost negligible (Belmont’s assets were essentially paper holdings in other concerns); it had been traded for only a short time for at most a few dollars a share.5
[74]*74In January of 1970 Michael Heller-man, who pleaded guilty and testified for the government, began steps to drive up the price of Belmont stock, first to $5 or $6 a share and then to nearly $50 a share. At that time two stock manipulators, Anthony Soldano and Fred Goodman, in concert with Hellerman, commenced acquiring substantially all of the 28,720 known publicly tradeable shares of Belmont. Goodman and Sol-dano executed their purchases ostensibly through the open market, using brokers who quoted prices for Belmont through the National Quotation Bureau’s pink sheets for over-the-counter securities. These purchases created the appearance of an active public market in the stock.
By early March, 1970 Goodman and Soldano had caused the market price of Belmont as quoted in the pink sheets to reach $15 a share. They did this primarily through directions to their brokers, who traded small quantities of the stock among themselves. In the meantime, Goodman and Soldano had acquired control, they believed, of all the outstanding stock.
At this point Hellerman’s role became paramount. According to his testimony, he already had an understanding with Dioguardi that “whatever I did in the future, ... he would have 25 per cent.” It had also been agreed between Hellerman, on one side, and Goodman and Soldano on the other that once the price of Belmont stock reached $15, Hel-lerman and his associates would purchase all the stock at the $15 level, with a $5 per share kickback, prior to further manipulation upwards. In confirming this arrangement with Goodman and Soldano, Hellerman took Soldano to Dioguardi’s office “to make sure it was on the record.”
According to Hellerman, it was at this time in early March that he brought Os-trer into the scheme, although the two were only recently acquainted. Ostrer agreed to commit himself to buy 14,000 shares of Belmont at $15 a share ($210,000 total), with the understanding that he would split any future profits with Hellerman, that Hellerman would guarantee him against loss, and that a loan of the purchase money would be arranged so that he would not have to “lay out a quarter” of the $210,000. Purchase orders in Ostrer’s name or in his behalf were to be made through various New York Stock Exchange firms.
Ostrer then placed orders in his own name and in his sister’s for 14,000 shares of Belmont. However, most Exchange firms which he approached refused to accept his orders, and he was forced to place relatively large block orders through firms where brokers were already in league with Hellerman.6
Contemporaneously, Hellerman made arrangements with others to purchase the remaining 14,000 or so shares of Belmont. These individuals were able to pay the selling brokers (at the $15 a share price), but Ostrer was unable to raise the $210,000 needed to “hold up” his end of the deal, a circumstance which left his brokers unpaid. According to Hellerman, he thereupon obtained a loan for Ostrer through Dioguardi. The funds, totalling $60,000, came from Hickey DiLorenzo, at an interest rate of íVz% a week. DiLorenzo also demanded and received $24,000 from Hellerman [75]*75for this favor (part of the kickback profits already made). In addition, Heller-man also advanced Ostrer $52,500, and Ostrer obtained the balance he needed from other sources.
Thereafter, from the end of March through late April, 1970, Hellerman directed purchases' and sales of Belmont stock at ever-increasing prices among the individuals and brokers whom he controlled. He kept Dioguardi, Ostrer, and DiLorenzo informed as the price rose. He also arrranged for Ostrer to sell off enough stock, through a nominee, to repay the $60,000 loan from Di-Lorenzo — with a $1700 profit left over which he split with Ostrer. By the end of April he had received approximately $140,000 in kickbacks from Goodman and Soldano. He gave $30,000 to Dio-guardi, and invested $9,000 more in a business in which Dioguardi had an interest.
In early May, 1970, the scheme failed. The president of Belmont through a broker unknown to the manipulators, began to sell heavily his own “investment” stock in the corporation. The market was unable to absorb the sales, and Hellerman was unwilling tp buy the stock and could not find 'other purchasers. Consequently the ¡market for Belmont collapsed, leaving Ostrer (among others) with large quantities of unsold stock. Ostrer then tried to bold Hellerman responsible for his losses. Hellerman became worried because Di-Lorenzo took Ostrer’s side. Dioguardi subsequently arbitrated the dispute to some extent, and arranged for partial compensation to Ostrer to the sum of $25,000.
At trial Dioguardi called no witnesses. and based his defense primarily on cross-examination going to the lack of credibility of the government’s major witnesses, who were all accomplices. Ostrer did not testify but he did call two witnesses whose testimony indicated that Ostrer had been a “victim” of Hel-lerman’s machinations.
About ten days after trial, Dioguardi received a letter from one of the jurors, Miss Genena Rush, a nurse’s aide employed at Flower Fifth Avenue Hospital in New York City. The letter was written on stationery bearing the zodiac sign of Libra, and on one page the legend that it was “the heavenly house under which I was born.” The juror wrote of her clairvoyant powers which enabled her to see that Dioguardi was basically a good person. She stated her belief that he was guilty, “Your mistake your guilty,” and questioned him about Heller-man, “Why you let such a relationship exist between you and a man like Heller-man?,” and called upon him to repent, “One word appear before me repent. If you repent and run a clean business it is the good within you that will save you, and you will gain what you have lost.” Miss Rush stated that
I have eyes and ears that I can see things before it happen. I can tell you about other and what they are thinking and doing,
and that her eyes
are only partly open .... Unfortunate, a curse was put upon them some years ago. I have some people working on them.
The letter is reproduced in full in the margin.7
[76]*76Dioguardi’s attorneys sent copies of the letter to seven psychiatrists, all of whom responded (one in an affidavit) to the effect that, in their opinion, what Miss Rush had written indicated hallucinatory tendencies, symptoms of possible psychosis, paranoia, and grandiosity, and in general an inability to appreciate reality without fantasizing.8 The psychiatrists also pointed out that further psychiatric analysis was needed before a diagnosis could be ventured with any certainty, or before it could be said that Miss Rush’s infirmities, whatever their nature and extent, might have rendered her unable to comprehend the proceedings at trial.9 The psychiatrists were given no information about the [78]*78juror or about the trial and the issues, and the court had forbidden anyone to seek to interview her.
On the basis of Miss Rush’s letter and the opinions of the psychiatrists, Dioguardi and Ostrer moved pursuant to Rule 33, F.R.Crim.P., for a new trial or in the alternative, for an evidentiary hearing on the competency of Miss Rush as a juror. They asserted that an uncontroverted showing of ineompeteney had been made out, in violation of 28 U.S.C. § 1865(b)(4) and their constitutional rights.10
Judge Edelstein, after hearing oral arguments and receiving briefs, denied the motion for a new trial and for further investigation of the juror’s competency on April 12, 1973, and later filed a thorough and considered opinion on July 18, 1973. 361 F.Supp. 954. He stated:
Moreover, there was nothing in the demeanor of the juror during voir dire, trial or deliberations to indicate that she was anything but competent to serve on the jury. On voir dire, the jurors were asked group questions in an effort to elicit from them their feelings of bias or prejudice which would prevent them from rendering a fair and impartial verdict, [footnote omitted] In direct colloquy with me, the juror answered directly and responsively, stating that she understood my questions and comments, and specifying the particular one which applied to her. Nothing in her responses and demeanor indicated that her reasoning abilities or mental processes were deficient. Indeed, her ability to recall my questions applicable to her, conveyed the opposite impression. Likewise, during the three weeks of trial and three days and nights of deliberations, I did not notice anything unusual about her. Nor was anything unusual concerning her brought to my attention by either the attorneys or jurors.
Examination of the juror on the voir dire had disclosed that she was then employed by Flower Fifth Avenue Hospital as a patient attendant assisting the nurses and had been so employed for four years. In answer to the court’s question as to whether any questions or comments applied to her, she stated that in 1944 she was employed by the Navy Department in Cleveland as assistant to the foreman in the cleaning department. Prior to her current hospital employment she was a silk finisher in a cleaning shop in the Bronx.
II.
A — Competency of Juror Rush
It is well settled that only clear evidence of a juror’s incompetence to understand the' issues and to deliberate at the time of his service requires setting aside a verdict. And only strong evidence that it is likely that the juror suffered from such incompetence during jury service will justify an inquiry into whether such incompetence in fact did exist. In our view the juror’s letter, and the essentially horseback uninformed opinions of the psychiatrists regarding the letter, fall considerably [79]*79short of justifying any further inquiry. Furthermore, the appellants have not cited a single authority which supports a grant of their motion on this record. Judge Edelstein was entirely correct in denying the motion.
Reluctance to inquire into the state of mind of any juror and into the conduct of the jurors during their deliberations rests on sound reasons.11 The rule against any inquiry whatever recognizes exceptions only where there is clear and incontrovertible evidence of incompetence shortly before or after jury service, clear evidence of some criminal act, or evidence of some “objective fact” of interna] impropriety.12 Even in the case of recent incompetence a hearing will be had to establish that it must have existed during jury service.
The strong policy against any post-verdict inquiry into a juror’s state of mind was stated by this court regarding an analogous situation in United States v. Crosby, 294 F.2d 928, 950 (2d Cir. 1961), cert. denied sub nom. Mittelman v. United States, 368 U.S. 984, 82 S.Ct. 599, 7 L.Ed.2d 523 (1962):
There are many cogent reasons militating against post-verdict inquiry
Nor have the courts favored any public or private post-trial inquisition of jurors as to how they reasoned, lest it operate to intimidate, beset and harass them. This Court will not accept their own disclosure of forbidden quotient verdicts in damage eases. McDonald v. Pless, 238 U.S. 264, [35 S.Ct. 783, 59 L.Ed. 1300]. Nor of compromise in a criminal case whereby some jurors exchanged their convictions on one issue in return for concession by other jurors on another issue. Hyde v. United States, 225 U.S. 347, [32 S.Ct. 793, 56 L.Ed. 1114], “If evidence thus secured could be thus used, the result would be to make what was intended to be a private deliberation, the constant subject of public investigation — to the destruction of all frankness and freedom of discussion and conference.” McDonald v. Pless, [238 U.S. 264 (1915)] at pages 267-268 [35 S.Ct. at page 784], [80]*80into jurors’ motives for decision. The jurors themselves ought not be subjected to harassment; the courts ought not be burdened with large numbers of applications mostly without real merit; the chances and temptations for tampering ought not be increased; verdicts ought not be made so uncertain.
We cited this language in Miller v. United States, 403 F.2d 77 (2d Cir. 1968) where the court also emphasized, at page 82, the importance of the dangers presented by inquiries that go beyond objective facts: “inhibition of jury-room deliberations, harassment of jurors, and increased incidence of jury tampering.” See also Stein v. New York, 346 U.S. 156, 178, 73 S.Ct. 1077, 97 L.Ed. 1522 (1953); McDonald v. Pless, 238 U.S. 264, 268, 35 S.Ct. 783, 59 L.Ed. 1300 (1915); and Mattox v. United States, 146 U.S. 140, 147-151, 13 S.Ct. 50, 36 L.Ed. 917 (1892).
With respect to post-verdict evidence of possible juror incompetency during the trial, courts have refused to set aside a verdict, or even to make further inquiry, unless there be proof of an adjudication of insanity or mental incompetence closely in advance of the time of jury service.13 Only when proof of this nature has been offered, or proof of a closely contemporaneous and independent posttrial adjudication of incompetency,14 have courts conducted hearings to determine whether the disability in fact affected the juror at the time of trial.
But absent such substantial if not wholly conclusive evidence of incompetency, courts have been unwilling to subject a juror to a hearing on his mental condition merely on the allegations and opinions of a losing party. In Peterman v. Indian Motorcycle Co., 216 F.2d 289 (1st Cir. 1954), the plaintiff, shortly after judgment against him in a civil suit for personal injury, moved for a new trial on the grounds “that certain information, discovered since the trial, disclosed the mental unfitness of the foreman of the jury, whose condition, if it had been known . . . would
have been a ground for disqualification.” Judge Wyzanski heard counsel on the motion and requested an offer of proof from the plaintiff’s attorney.
The offer of proof was . . . that the juror in question, because of his mental disturbance, has been receiving disability compensation from the Veterans Bureau; that he has difficulty in sleeping and concentrating; that his memory is not good; that he has had depressed periods during which he entertained the idea of suicide; that he has had to undergo treatment for anxiety reaction to a psychic episode expressed by auditory hallucinations; that he has been under the care of a psychiatrist for an extended period, with little prospect of an early overcoming of his difficulties. [Id., at 293.]
Judge Wyzanski held that the offer of proof was inadequate and denied the plaintiff’s motion15 The Court of Ap[81]*81peals for the First Circuit agreed, stating that:
Considering the strong policy against the too-ready impeachment of jury verdicts on the basis of such afterthoughts suggested by a disappointed litigant, . . . the trial judge cannot be held to have abused his discretion in declining to grant a new trial on this ground. [Id.]
See also United States ex rel. Daverse v. Hohn, 198 F.2d 934 (3rd Cir. 1952).
In light of this legal background, we do not believe appellants made enough of a case to justify further inquiry into the competence of Juror Rush. No evidence was offered of any history of mental instability on the part of Miss Rush, much less evidence of any adjudication of insanity or incompetence. Indeed, what we do know of her past, although it is little, reflects quite the contrary situation. She has held steady employment over the past four years as a nurse’s aide at Flower Fifth Avenue Hospital, and apparently had steady employment before that as well. The trial judge, as noted above, found the juror alert and responsive and he noted nothing unusual about her during the three weeks of trial and three days and nights of deliberation. Although the opinions of experts are not to be dismissed altogether, they were here of necessity formed in a vacuum, based on one piece of evidence, and fall far short of constituting the sort of “objective fact” which can justify inquiry into the internal workings of the jury. The fact that there is no evidence of harassment of Miss Rush or solicitation of the letter does not render irrelevant the policy considerations which forbid inquiry into the internal workings of the jury absent objective evidence of impropriety. In another case a letter could be fabricated or solicitation could be disguised; a'decision for appellants on this issue would therefore raise very real risks of “inhibition of jury room deliberations, harassment of jurors, and increased incidence of jury tampering.” Indeed, even where such a letter is as fully voluntary as the one in this case appears to be, it surely was not thought by its author tó be an invitation to “develop evidence by investigating the juror’s background or by persuading her to undergo a voluntary mental examination” — the suggestions of the dissent for possible proceedings on remand. We conclude that the action of the district court in denying the defendants’ motion was entirely proper.
B — Prosecutor’s Comments in Summation
The government prosecutor, in his summation, noted that, apart from the two quasi-character witnesses called by defendant Ostrer, the defendants had called no witnesses to contradict the factual content of the government’s case. Defense counsel objected to these remarks, and the appellants argue that the remarks were improper in that only they themselves (or co-conspirators whose testimony they could not compel) could have testified in contradiction to the government’s witnesses. We do not agree.
It is true that it has been frequently held impermissible for the prosecution to comment on a defendant’s failure to call witnesses where only the defendant could offer countertestimony or where the jury will “naturally and necessarily” interpret this as a comment upon the defendant’s silence, otherwise constitutionally protected. See, e. g., United States v. Lipton, 467 F.2d 1161 (2d Cir. 1972); United States v. Flannery, 451 F.2d 880 (1st Cir. 1971); United States v. Handman, 447 F.2d 853 (7th Cir. 1971); Desmond v. United States, 345 F.2d 225 (1st Cir. 1965).
However, this danger can be neutralized by a prompt corrective instruction to the jury. Such an instruction was given by Judge Edelstein. Moreover, this was not the close situation in which it was a question of a defendant’s word against the word of one other (cf. Handman, where the defendant was implicated solely by an inform[82]*82er’s testimony about a telephone conversation between himself and the defendant). Thus, even though many of the meetings between Hellerman, Ostrer, Dioguardi, and DiLorenzo were private, their activities also involved numerous stock brokers and other Wall Street figures, several of whom also testified at trial. See fn. 1, supra. Given the breadth of the operation, it was not improper for mention to have been made of the dearth of defense witnesses from so large a cast of characters. The record supports the conclusion that there were meetings between the persons involved in the Belmont stock manipulation at which more were present than the defendants and the government’s witnesses at trial, and that some of these persons could have been called to testify or at least that in many other ways defendants could have waged factual war with the detailed evidence of the government’s witnesses.
In United States ex rel. Leak v. Follette, 418 F.2d 1266 (2d Cir. 1969), cert. denied, 397 U.S. 1050, 90 S.Ct. 1388, 25 L.Ed.2d 665 (1970) which concerned similar comments by the prosecutor on the strength of the government’s case against the accused and on the lack of any contradictory evidence, we reviewed the many precedents which, in almost every instance, have “held that remarks concerning lack of contradiction are forbidden only in the exceedingly rare case where the defendant alone could possibly contradict the government’s testimony,” id., at 1269, and then concluded that
where the prosecutor confines himself to arguing the strength of his case by stressing the credibility and lack of contradiction of his witnesses, we will not be astute to find in this a veiled comment on the defendant’s failure to testify even if in practical fact, although not in theory, no one else could controvert them. [Id., at 1270.]
The defendants’ objections to the prosecutor’s comments in summation were properly denied.
C — Specific Charge on Accomplice Testimony
Both defendants argue that it was error for the trial court to have refused to instruct the jury specifically that the testimony of accomplices who were confessed perjurers or convicted felons was to be scrutinized with particular care. There is no merit to this argument. The trial court’s charge to the jury was amply cautionary on this point. A similar charge was recently sustained by us in United States v. Projansky, 465 F.2d 123, 136-137 and nn. 24-25 (2d Cir.), cert. denied, 409 U.S. 1006, 93 S.Ct. 432, 34 L.Ed.2d 299 (1972).
D — The Evidentiary Ruling
At one point in the trial Heller-man testified that Dioguardi had used some of the proceeds of the Belmont stock scheme to help pay off a mortgage on his summer home. Apparently this statement was incorrect. To help pay off the mortgage Dioguardi had used funds obtained through a prior stock manipulation, but one on which he had been acquitted at a previous trial. At the side bar, counsel for Dioguardi argued that the prosecution should correct Hellerman’s testimony. The trial court stated that correction was properly the responsibility of defense counsel. Dioguardi’s lawyer, however, was unwilling to raise the issue unless proof could also be introduced of the earlier acquittal. The trial judge at this point expressed himself somewhat ambiguously, and the parties differ whether we should read him as having refused to give a ruling in advance on the question whether he would allow proof of acquittal, holding that admissibility would depend on the course of testimony, or as having held that proof of acquittal would not in any case toe admissible in this context. In either event, as a consequence of the trial judge’s action, Hellerman’s testimony was allowed to stand, and the issue was not raised again.
Dioguardi claims that the court’s ruling or failure to rule was improper and [83]*83that it permitted false testimony to reach the jury. This claim, while perhaps technically valid, is essentially groundless. The circumstances behind the controversy at issue were never pursued in testimony in open court. No facts behind it were ever in evidence. While the record does reveal occasional allusions to the prior stock manipulation, the so-called “Imperial deal,” none of these could be considered prejudicial in reference to Dioguardi. Hellerman’s statement was de minimis in view of the other evidence. No reversible error was committed by the trial court under the circumstances. It was a matter fully within the trial court’s discretion. See United States v. Kahn, 472 F.2d 272, 282 (2d Cir.), cert. denied, 411 U.S. 982, 98 S.Ct. 2270, 36 L.Ed.2d 958 (1973).
E — Consecutive Sentences for Stock Fraud
Lastly, Dioguardi claims that it was improper for the trial court to impose separate consecutive sentences and separate fines upon him for the violations in counts 16 and 17 of the indictment. Count 16 involved confirmation of the purchase in Ostrer’s name, with Dioguardi’s approval, of 2000 shares of Belmont stock through Bruce & Co. on March 10, 1970. Count 17 involved confirmation of the similar purchase of 3500 shares through Kelsey & Co. on March 11th. See fn. 6, supra. Diorguardi argues that these purchases, and their confirmations, were part of a single transaction, namely Ostrer’s purchasing half (14,000) of the supposed outstanding shares of Belmont stock, and that hence they cannot constitute separate violations of the securities laws.
It is true that there has been debate in the past over whether such transactions constitute a multiple offense, the essence of the violation being illegal use of the mails, or a single offense, the essence being fraud. See 3 Loss, Securities Regulation 1521 (2d ed., 1961); and also United States v. Hughes, 195 F. Supp. 795 (S.D.N.Y.1961). However, recent litigation involving fraud under the securities laws has resolved this debate in favor of the position that each transaction in a securities fraud case constitutes a separate offense. Sanders v. United States, 415 F.2d 621 (5th Cir. 1969), cert. denied, 397 U.S. 976, 90 S.Ct. 1096, 25 L.Ed.2d 271 1970); see also United States v. Binstock, 37 F.R.D. 13 (S.D.N.Y.1965). This position acknowledges the fact that activity such as the kind Dioguardi engaged in here in relation to the two Ostrer purchases on March 10th and 11th was fraudulent in each instance, not necessarily in respect to the scheme as a whole, nor even necessarily in respect to the sellers on those two days (who may have been coconspirators or perhaps simply others pleased to sell at a gain), but in respect to the investing public. Thus although a situation can be envisioned in which consecutive sentences on multiple fraud convictions would be questionable, cf. United States v. Brown, 36 F.R.D. 207 (D.D.C.1964), in the instant case the determination and sequence of the sentences imposed on defendant Dioguardi were matters within the discretion of the trial court. See Sanders v. United States, supra, 415 F.2d at 626, and the cases there cited. The consecutive sentences on counts 16 and 17 were therefore proper.
Judgments of conviction affirmed.