BOGGS, Circuit Judge.
Frank Runnels (Runnels), former president of Local 22 of the United Automobile Workers (UAW) and Arnold Shapero (Shapero), an attorney, appeal their convictions for mail fraud and conspiracy to commit mail fraud. Runnels was charged with committing mail fraud by obtaining money through false and fraudulent pretenses and by depriving the members of Local 22 of his fair and honest services. Shapero was charged with conspiring to commit mail fraud by bribing Runnels and by defrauding the members of Local 22 of their intangible right to fair and honest union representation. The doctrine that mail fraud could include deprivation of “intangible rights” was struck down by the Supreme Court after the convictions of Runnels and Shapero. However, as we hold that the jury necessarily found that Runnels, in breaching his fiduciary duty to Local 22 by taking a bribe, violated 18 U.S.C. § 1341 by depriving Local 22 of an economic benefit which properly belonged to it, we affirm these convictions.
I
In May or June of 1979, Andrew Schlesinger (Schlesinger) arranged for Shapero to pay Runnels $10,000 immediately and $1,700 per month thereafter in return for referring workers’ compensation cases to Shapero’s law firm. An attorney from Shapero’s firm would attend retirees’ meetings, at which Runnels would discuss retirees’ rights in general and workers’ compensation in specific, and refer the members to the attorney. After prospective clients were signed up at retirees’ meetings, workers’ compensation claims were mailed to Lansing, Michigan. As part of the agreement, Schlesinger was placed on the firm's payroll. However, in June 1980, Shapero told Schlesinger that the arrangement had changed and that Schlesinger was to stay away from Runnels and Local 22, but would continue to draw a salary. [1185]*1185At trial, Shapero testified that Runnels caused this change, in the belief that Schlesinger was not conveying the full $1,700 per month. Runnels asked for $2,000 per month in cash, to be paid directly to him.
According to Shapero, Runnels missed a number of retirees’ meetings due to illness in 1980-1981, causing a drop in the number of applicants for workers’ compensation. Shapero told Runnels that he would receive his $2,000 only for those months when he addressed the retirees’ meeting. In 1988, Runnels left Local 22 to become a UAW regional director, at which point the payments stopped.
In January 1986, Runnels was charged with violating 18 U.S.C. § 371 (conspiracy) and 18 U.S.C. § 1341 (mail fraud). Following a jury trial, he was found guilty. He appeals that verdict.
Shapero was charged with conspiracy to commit mail fraud, in violation of 18 U.S.C. § 371 and § 1341. He pled guilty pursuant to a plea agreement under Rule 11, Fed.R. Crim.P., which provided for a maximum eighteen month prison term. As part of the agreement, Shapero cooperated with the government and testified at Runnels’s trial.
Shapero moved to set aside his plea, on the grounds that the information failed to state a cause of action, and that the factual basis of the guilty plea was insufficient. The district court denied his motion and sentenced Shapero to eighteen months of imprisonment with all but the first six months suspended, and two years of probation.
II
The relevant portion of 18 U.S.C. § 1341 bans “any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations or promises_” The Supreme Court has stated that “[t]he elements of the offense of mail fraud under 18 U.S.C. ... § 1341 are (1) a scheme to defraud, and (2) the mailing of a letter, etc., for the purpose of executing the scheme.” Pereira v. United States, 347 U.S. 1, 8, 74 S.Ct. 358, 362, 98 L.Ed. 435 (1954). See also United States v. Street, 529 F.2d 226, 228 (6th Cir.1976).
The mail fraud statute has been applied to a range of circumstances. For instance, the scheme need not have been actually successful in order for a mail fraud violation to have occurred. See, e.g., Erwin v. United States, 242 F.2d 336 (6th Cir.1957); Gridley v. United States, 44 F.2d 716 (6th Cir.1930), cert. denied, 283 U.S. 827, 51 S.Ct. 351, 75 L.Ed. 1441 (1931). Criminal liability for false pretenses, which the mail fraud statute was intended to reach, was consistently predicated upon the defendant’s taking or attempted taking of some economic benefit from the scheme’s victim, during the period of the mail fraud statute’s enactment and amendment, 1870 to 1909. See 35 C.J.S. False Pretenses §§ 6, 26 (1960), and cases cited therein. Decisions permitting convictions despite the absence of economic loss still required that the defendant deprive the victim of some economic benefit. See generally, Comment, The Intangible-Rights Doctrine and Political-Corruption Prosecutions Under the Federal Mail Fraud Statute, 47 U.Chi.L.Rev. 562, 572-78 (1980), and cases listed at 572-78.
Thus, cases decided under 18 U.S.C. § 1341 prior to 1973 involved some transfer or planned transfer of economic value to the defrauder from the victim. See Parr v. United States, 363 U.S. 370, 80 S.Ct. 1171, 4 L.Ed.2d 1277 (1960); United States v. Beitscher, 467 F.2d 269 (10th Cir.1972); United States v. Randle, 39 F.Supp. 759, 760 (W.D.La.1941). After 1973, courts began to permit conviction of corrupt politicians, without finding a direct transfer of economic value to the politician from the populace, by finding that the citizens had been defrauded of their intangible right to fair and honest government.1 See United States v. Mandel, 591 F.2d 1347, 1359-60, on reh’g, 602 F.2d 653 (4th Cir.1979), cert. [1186]*1186denied, 445 U.S. 961, 100 S.Ct. 1647, 64 L.Ed.2d 236 (1980); United States v. Keane, 522 F.2d 534 (7th Cir.1975), cert. denied, 424 U.S. 976, 96 S.Ct. 1481, 47 L.Ed.2d 746 (1976). Courts have also applied the intangible rights doctrine in corporate and labor cases. See United States v. Barta, 635 F.2d 999, 1005-07 (2d Cir.1980), cert. denied, 450 U.S. 998, 101 S.Ct. 1703, 68 L.Ed.2d 199 (1981) (corporate); United States v. Bohonus, 628 F.2d 1167 (9th Cir.), cert. denied, 447 U.S. 928, 100 S.Ct. 3026, 65 L.Ed.2d 1122 (1980) (same); United States v. Price, 788 F.2d 234 (4th Cir.1986), vacated, — U.S. —, 107 S.Ct. 3254, 97 L.Ed.2d 754 (1987) (in light of McNally v. United States, 483 U.S. —, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987)) (labor); United States v. Local 560, 780 F.2d 267 (3d Cir.1985), cert. denied, — U.S. —, 106 S.Ct. 2247, 90 L.Ed.2d 693 (1986) (same); United States v. Boffa, 688 F.2d 919 (3d Cir.1982), cert. denied, 460 U.S. 1022, 103 S.Ct. 1272, 75 L.Ed.2d 494 (1983) (same).
The Supreme Court has recently held, in McNally v. United States, 483 U.S. —, 107 S.Ct. 2875, 2881, 97 L.Ed.2d 292 (1987), that § 1341 only proscribes conduct which transgresses property rights, not conduct which transgresses intangible rights.
Ill
The intangible rights doctrine retains no vitality after McNally. However, an alternative rationale, based on the fraud that occurs when a fiduciary breaches his duty by appropriating an economic benefit that properly should be the principal’s, leads us to permit Runnels’s sentence for violating § 1341 to stand.
Runnels had a fiduciary duty to Local 22 and its members. The existence of the fiduciary duties of union officials is well established.2 See United States v. Boffa, 688 F.2d at 930 (“There is little doubt that union officials owe union members a fiduciary duty [under § 501(a) of the Labor Management Disclosure Act, 29 U.S.C. § 501(a)].”); Morrissey v. Curran, 650 F.2d 1267, 1275 (2d Cir.1981) (“The fiduciary standards for union officers impose liability upon them when they approve their receipt of excessive benefits, significantly above a fair range of reasonableness.”); Farrington v. Benjamin, 468 F.Supp. 343, 350 (E.D.Mich.1979) (“Section 501(a) confers fiduciary status on union officers who deal with property and funds of the union.”); United States v. Hoffa, 205 F.Supp. 710 (S.D.Fla.1962), cert. denied sub nom. Hoffa v. Lieb, 371 U.S. 892, 83 S.Ct. 188, 9 L.Ed.2d 125 (1962) (by implication). Inasmuch as § 501(a) of the Labor Management Disclosure Act of 1959, 29 U.S.C. § 501(a), places a fiduciary duty on union officials to “account to the organization for any profit received ... in whatever capacity in connection with transactions conducted by him ... on behalf of the organization,” it is clear that Runnels violated his fiduciary duty by failing to turn over to Local 22 or use for its benefit the payments he received from Shapero.3
[1187]*1187In the vast majority of those intangible rights doctrine cases that involve fiduciaries, the defendant has derived some economic benefit, such as accepting a bribe or kickback. See United States v. Curry, 681 F.2d 406 (5th Cir.1982) (diversion of money donated to political organization for personal expenses); United States v. Bohonus, 628 F.2d 1167 (9th Cir.), cert. denied, 447 U.S. 928, 100 S.Ct. 3026, 65 L.Ed.2d 1122 (1980) (kickback from insurance premiums); United States v. Mandel, 591 F.2d 1347, 1360, on reh’g, 602 F.2d 653 (4th Cir.1979), cert. denied, 445 U.S. 961, 100 S.Ct. 1647, 64 L.Ed.2d 236 (1980) (clothing, diamond bracelet, and assignment of land interest); United States v. Bush, 522 F.2d 641, 651 (7th Cir.1975), cert. denied, 424 U.S. 977, 96 S.Ct. 1484, 47 L.Ed.2d 748 (1976) ($162,000 in “consultant” fees); United States v. Isaacs, 493 F.2d 1124, 1150 (7th Cir.), cert. denied, 417 U.S. 976, 94 S.Ct. 3183, 41 L.Ed.2d 1146 (1974) (securities gains of $159,800 on an outlay of $15,079). The existence of such a bribe or kickback makes it unnecessary to invoke the intangible rights doctrine. The fiduciary’s acquisition of an economic benefit which properly belongs to the principal, through an intentional breach of a fiduciary duty owed to the principal, is in itself sufficient to support a finding of guilt under 18 U.S.C. § 1341.
To understand why this is so, it is useful to consider the relevant elements of a conviction under § 1341 in this case: 1) a scheme to 2) obtain by deceit 3) money or property.4 First, the agreement between the breaching fiduciary and the person paying him constitutes a scheme. Second, the breach itself provides the necessary deception. See Strong v. Repide, 213 U.S. 419, 29 S.Ct. 521, 53 L.Ed. 853 (1909); Richardson’s Executor v. Green, 133 U.S. 30, 10 S.Ct. 280, 33 L.Ed. 516 (1890). Third, the bribe or undue profit acquired through a breach of a fiduciary duty does not properly belong to the breaching fiduciary.
This last point, that fiduciaries have no right to an economic benefit acquired through a breach of fiduciary duty, is well established. Rather, the benefit properly belongs to the entity to whom the fiduciary has a duty.5 See Jackson v. Smith, 254 U.S. 586, 587-88, 41 S.Ct. 200, 201, 65 L.Ed. 418 (1921) (fiduciary is liable to principal for profits gained through exploitation of a conflict of interest); Ohio Drill & Tool Co. v. Johnson, 625 F.2d 738, 742 (6th Cir.1980) (corporation director, by placing self in a position of conflicting economic loyalties, violates fiduciary duty and is strictly accountable for expenses charged to corporation and profits gained); Haberman v. Murchison, 335 F.Supp. 286, 292 (S.D.N.Y.1971), aff'd, 468 F.2d 1305 (2d Cir.1972) (if corporation director received premium for resignation, receipt of premium was breach of fiduciary duty making director liable to corporation for premium). See generally, 19 C.J.S. Corporations § 786, and cases cited therein (1940).
Thus, the economic deprivation to the principal which occurs when the fiduciary knowingly breaches his duty by accepting a bribe, the value of which properly belongs to the principal, is itself sufficient to support a finding of taking of value. The breaching fiduciary has acquired the bribe only through his authority as fiduciary, not in his private capacity. For example, Governor Kemer, in the transactions at issue in United States v. Isaacs, 493 F.2d 1124, 1150 (7th Cir.), cert. denied, 417 U.S. 976, 94 S.Ct. 3183, 41 L.Ed.2d 1146 (1974), was not bribed to provide private legal service. Rather, he was bribed to influence his behavior as governor. The bribe is therefore a benefit which properly belongs to the country, state, company, or union, which is the principal, rather than the official, officer, or employee, who is merely a fiduciary-[1188]*1188agent. Cf. 18 U.S.C. § 3612 (money used to bribe a Federal official and tendered in evidence is forfeited to federal government).
A constructive trust confers upon a non-possessory property owner an equitable interest superior to the non-owning possessor’s interest, in order to prevent unjust enrichment. See, e.g., In re N.S. Garrott & Sons, 772 F.2d 462, 467 (8th Cir.1985). The conditions in which a fiduciary’s breach creates a constructive trust illuminate this analysis, which is based on the deprivation by a fiduciary of an economic benefit (“benefit deprivation analysis”).
[Fiduciaries] must employ the principal’s property for his benefit and not for the fiduciaries’ selfish advantage. They are held to the highest amount of loyalty and good faith, are required to exclude all selfish interest, [and] are prohibited from putting themselves in positions where personal interest and representative interest will conflict_ If the ... fiduciary violates any one of these or his other duties to his beneficiary ór his principal and thereby acquires ownership of property ... he may be charged ... as a constructive trustee ... with respect to the property in question.
Bogert, 4 Trusts & Trustees, § 481 (2d ed. 1978). This is why
it has been repeatedly held ... that public officials and employees serving interests in conflict with those of the United States for their own gain hold the funds they receive, no matter what the source, in constructive trust for the government.
United States v. Podell, 572 F.2d 31, 35 (2d Cir.1978) (citations omitted). As the Supreme Court stated in United States v. Carter, 217 U.S. 286, 30 S.Ct. 515, 54 L.Ed. 769 (1910),
[t]he larger interests of public justice will not tolerate, under any circumstances, that a public official shall retain any profit or advantage which he may realize through the acquirement of an interest in conflict with his fidelity as an agent [of the United States.] If he takes any gift, gratuity or benefit in violation of his duty, or acquires any interest adverse to his principal without a full disclosure, it is a betrayal of his trust and a breach of confidence, and he must account to his principal for all he has received.
217 U.S. at 306, 30 S.Ct. at 520. Thus, as a fiduciary, one must account to, that is, pay over to, one’s principal the property held in the constructive trust. This is why the court in Morrissey v. Curran, 650 F.2d 1267, 1271 (2d Cir.1981), upon determining that union officials were constructive trustees of funds acquired through breaches of their fiduciary duty, as defined in § 501(a) of the Labor Management Disclosure Act of 1959, 29 U.S.C. § 501(a), required the officials to make this type of accounting.
We recognize that situations can be hypothesized in which a fiduciary who knowingly breaches his duty by accepting a bribe or kickback arguably does not deprive the principal of an economic benefit, as would have been the case if Runnels had not pocketed the payments from Shapero, but rather had demanded lower legal fees for the members of Local 22, or had spent all of the payments on furnishings for the union hall, or if Governor Kemer had donated the value of the bribes he received to the Illinois general fund. However, under such circumstances there simply has not been an economic fraud, even if the fiduciary’s behavior is distasteful or even independently criminal.
IV
A
Runnels was convicted under a jury instruction which included the intangible rights doctrine, an interpretation of the mail fraud statute which permits a finding of guilt if a person defrauds others of their intangible right to fair, honest and efficient representation. The Supreme Court in McNally v. United States, 483 U.S. —, 107 S.Ct. 2875, 97 L.Ed.2d 292 (1987), held the intangible rights doctrine to be invalid. Thus, we now regard the trial court’s jury instruction on the intangible rights doctrine as erroneous.
[1189]*1189However, the instruction is not necessarily reversible error. When several theories are presented to a jury and one theory is determined on appeal to be invalid, a conviction which was not based separately and specifically on a valid theory usually cannot stand. This is because it is impossible to tell which theory the jury followed. United States v. Alsondo, 486 F.2d 1339, 1345 (2d Cir.1973), rev’d on other grounds sub nom. United States v. Feola, 420 U.S. 671, 95 S.Ct. 1255, 43 L.Ed.2d 541 (1975); Nicola v. United States, 72 F.2d 780, 787 (3d Cir.1934). However, appellate courts have affirmed convictions based on an erroneous instruction where the jury’s verdict necessarily demonstrates that it found against the defendants on all the facts necessary to convict on a proper theory or instruction which was also before the jury.
In United States v. Jacobs, 475 F.2d 270 (2d Cir.), cert. denied sub nom. Lavelle v. United States, 414 U.S. 821, 94 S.Ct. 116, 38 L.Ed.2d 53 (1973), the defendants were charged with conspiring to violate 18 U.S. C. §§ 2314 and 2315 based on their attempts to sell stolen United States Treasury bills. The count was submitted under two theories. The first, which upon appeal was determined to be erroneous in part due to insufficiency of the evidence, was that the defendants conspired to transport stolen securities to Washington, D.C., for presentation to the United States Treasurer. The court held that there was no evidence that the defendants thought that the bills, which would be perforated and voided by a local bank, would travel to Washington as securities. The second theory was that the defendants conspired to defraud the United States. The court stated that
this case falls outside the general rule [that if the jury received both a valid and an erroneous instruction, it is impossible to tell which the jury has followed and the judgment must be reversed]. If the jury found a conspiracy on what we deem the erroneous view that the evidence supported a conclusion that [defendants] had entered into an agreement to have stolen treasury bills transported to Washington for payment by the United States, it would have found every element necessary to support a conclusion that the defendants had entered into an agreement to defraud the United States by causing it to redeem the bills from a recipient from a thief rather than from the rightful owner. Whether the jury found [the defendants] guilty on the first theory submitted to it, or on the second, or on both, there is thus no uncertainty that the jury found every fact necessary for a valid conviction. ...
475 F.2d at 283-84 (emphasis added).
In United States v. H & M, Inc., 562 F.Supp. 651, 660 (M.D.Pa.1983), a criminal antitrust case, the court submitted the case to the jury on two theories, the first based on the presence in interstate commerce of “motopaving,” an asphalt-based paving product, and the second based on the effect on interstate commerce of sales of moto-paving. The defendants argued in post-trial motions that the court’s jury instruction erroneously excluded their contention that motopaving was not in the flow of interstate commerce. The court stated that
[ajssuming without deciding that the court erred in instructing the jury ... no reversible error was committed. The general rule is that where alternative theories are presented to the jury, one erroneous and prejudicial, the error is prejudicial since it is impossible to tell which theory the jury followed.
There is no prejudice, however, when, in order for the jury to find an essential element of crime based on the erroneous instruction, it must necessarily have found every fact essential to support a finding of the same element based on the alternative, correct charge. ... For the jury to have found interstate commerce on the basis of the court’s instruction on the “flow of interstate commerce” theory, it must necessarily have found that a principal ingredient of motopaving in the four-county area was liquid asphalt which was transported in interstate commerce. Such finding of facts also establishes every element necessary to a finding of inter[1190]*1190state commerce under the court’s instruction on the “affect [sic] on interstate commerce” theory. Consequently, regardless of the theory on which the jury based its finding, it is evident that the jury found every fact necessary to establish the requisite nexus....
562 F.Supp. at 660 (emphasis added) (citations omitted).
Jacobs and H & M demonstrate the propriety of affirming a conviction even when a jury has been presented with a single count based on two theories, one of which turns out to be invalid. Additionally, there are many cases which demonstrate the propriety of affirming convictions when the jury has been presented with multiple counts, one of which turns out to be invalid. For example, in United States v. Reid, 517 F.2d 953 (2d Cir.1975), the defendants, in the course of a robbery, stole a revolver belonging to a Drug Enforcement Agency officer and shot him with it. The jury was instructed that it could convict the defendants of unlawful use of a firearm in the commission of a felony as charged in Count Three of the jury instructions if it found that the revolver was used in committing one or more felonies charged in Counts One, Two, Four or Five. The jury did convict the defendants on Count Three, as well as Counts One and Two, but acquitted them on Count Five. On appeal, Count Two was vacated, raising the possibility that the conviction on Count Three had been based on that erroneous conviction. The court stated that
[w]hile the general principle is that ... “[w]here two instructions are given to the jury, one erroneous and prejudicial and the other correct, it is impossible to tell which one the jury followed and it constitutes reversible error,” ... this is subject to an exception when the verdict gives assurance that no prejudice in fact occurred. Here Count One charged not merely assault but [also] assault “by use of a deadly and dangerous weapon, to wit, a revolver.” In finding the defendants guilty of that charge, the jury necessarily found all the facts required for a conviction on the third count. It is thus immaterial that the jury may have considered the felony charged in Count Two also to have been a predicate.
517 F.2d at 965 (citations and footnote omitted).
Similarly, in United States v. Baratta, 397 F.2d 215 (2d Cir.), cert. denied, 393 U.S. 939, 89 S.Ct. 293, 21 L.Ed.2d 276 (1968), the defendants, appealing their convictions on both the substantive crime of narcotics importation and conspiracy to import narcotics, alleged that the trial court failed to instruct the jury that knowledge of illegal importation is an essential element of a conspiracy. The Second Circuit stated that
[i]n the present case it is conceded that the trial court did not specifically instruct as to the requirement of knowledge of illegal importation on the conspiracy count.... On the other hand, it is also not disputed that the charge adequately informed the jury as to the knowledge of illegal importation required for the substantive crime and that the trial court did charge that the jury must find that each defendant “willfully and knowingly joined a conspiracy to violate that substantive law relating to the sale of narcotics.” Furthermore, in launching into his discussion of the substantive aspects of the offenses charged, the trial court stated:
The third element that must be proven beyond a reasonable doubt is that the narcotic drugs were illegally imported into the United States; and, fourth, and this, too, must be proven beyond a reasonable doubt, that each defendant knew that these narcotic drugs had been illegally imported into the United States....
Although these statements do not take the place of an explicit treatment of the knowledge of illegal importation required for conviction on the conspiracy count, so far as these defendants were concerned any defect in the charge as to this element was cured by the jury’s finding of the guilt of all appellants of both the substantive offense and the conspiracy. Since the instruction as to knowledge of [1191]*1191illegal importation with respect to the substantive offense was more than sufficient, and since the jury found all appellants guilty of the substantive offense, they must have found that each of them had the requisite knowledge of illegal importation....
397 F.2d at 225-26 (citations omitted). See also United States v. Dickens, 524 F.2d 441, 446 (5th Cir.1975), cert. denied sub nom. Glenos v. United States, 425 U.S. 994, 96 S.Ct. 2208, 48 L.Ed.2d 819 (1976).
This line of cases demonstrates that a conviction based on an erroneous instruction may be affirmed if the jury necessarily found every factual predicate for a conviction under a proper theory. Therefore, if the combination of the jury instruction at Runnels’s trial and the verdict necessarily demonstrate factual findings sufficient to support a guilty verdict under the benefit deprivation analysis given above, we will affirm. “This court may affirm on any ground squarely presented on the record.” United States v. Brock, 571 F.2d 480, 483 n. 3 (9th Cir.1978) (citation omitted).
B
We are aware of the dangers of affirming a criminal conviction on a theory not properly advanced at trial. See United States v. Castillo-Felix, 539 F.2d 9, 13 (9th Cir.1976). Perhaps the gravest danger is that of denying a defendant the opportunity to present his arguments fully upon the issues vital to the jury’s verdict. Although we may affirm on any ground squarely presented on the record, we are willing to do so in this case only because we are convinced, upon careful examination of the record, that the issues of the payments to Runnels and of his fiduciary relationship to Local 22 were presented at trial and fully argued to the jury.
Under the intangible rights doctrine, a defendant can be convicted only if it is proven that he defrauded others of their intangible right to fair, honest, faithful and disinterested representation by not applying his independent judgement to the decisions at issue. See Mandel, 591 F.2d at 1362. This can be established by showing that the representative has been suborned.
In the present case, the only method of subornation presented to the jury was by payments from Shapero to Runnels, and earlier payments from another attorney. The existence and importance of those payments was well argued. Indeed, the payments, and the character of the witnesses who testified about the payments, were the primary issues argued by Runnels’s counsel in his closing summation on the mail fraud count. No more than seven pages of a thirty-nine page summation on the mail fraud count passed without argument contesting these issues. For example:
Have you seen one bit of evidence that has been put to you by the prosecution of one red cent that Frank Runnels took in this case?.... They certainly went after Frank Runnels and where in heaven’s name is there one iota of evidence put in this case that you can say, “Aha! That’s where he put the money,” or “Aha! This is where he put part of this money.” Not one bit of that ever came forward. A total void.
Transcript at 488-89.
The district court judge, in giving Runnels’s theories of defense to the jury, stated that
Defendant Runnels claims that he never accepted any monies whatsoever from anyone.... On this theory, Frank Runnels claims that he is totally innocent of the charge because he received no monies of any kind, nature and description, therefore, he is entitled to a verdict of not guilty at your hands.... [On his second theory, Runnels claims that neither Local 22 nor the UAW had any right to] any monies that the plaintiff, United States of America, claims was [sic] paid to him by the attorneys or the agents for the attorneys, which defendant vehemently denies ever receiving....
Transcript at 532-34.
The prosecution also put the payments at or near the core of its argument. In his summation, the Assistant U.S. Attorney stated that
as Walter Reuther said in his letter, the members [of Local 22] pay their dues. [1192]*1192And that is where [Runnels’s] salary comes from, not supplemented on the side by people who he cuts independent deals [sic]. That is the heart and soul of the conspiracy and it is also the heart and soul of the scheme or artifice to defraud laid out in the substantive count of mail fraud. That is what Mr. Runnels did was conceal his involvement in the recommendation of this law firm for one and only one reason, his own personal financial gain.
Transcript at 511.
The jury could only have found Runnels guilty under the intangible rights doctrine by concluding that Runnels, though a fiduciary of Local 22, had accepted payments from Shapero and others. These payments were the only method of subornation presented at the trial. Thus, it is inescapable that the jury concluded that Runnels accepted payments.
A fiduciary’s knowing deprivation, through a breach of his fiduciary duty, of an economic benefit due his principal will support a conviction for violation of the mail fraud statute, as we have shown in Section III of this opinion. If Runnels accepted the payments, as the jury necessarily concluded, then he took money which belonged to Local 22 as a matter of law, and violated the mail fraud statute under either the intangible rights doctrine or under the benefit deprivation analysis. “[T]here is thus no uncertainty that the jury found every fact necessary for a valid conviction....” United States v. Jacobs, 475 F.2d 270, 283-84 (2d Cir.), cert. denied sub nom. Lavelle v. United States, 414 U.S. 821, 94 S.Ct. 116, 38 L.Ed.2d 53 (1973).
Based upon our review of the record, the strength of the evidence supporting the jury’s necessary finding that Runnels did accept payments, and the strong indications in the record that Runnels’s acceptance of the payments was vigorously contested at trial, we decline to reverse the district court's judgment entered on the jury’s verdict.
y
McNally is distinguishable from the present cases. The differences between the facts in McNally and those in the present cases are such as to permit our affirmance of the convictions of Runnels and Shapero.
The crucial difference between the facts in McNally and those in the present cases is that in McNally the money at issue, insurance premiums which were required to be shared with an insurance agency in which McNally had an ownership interest, was not shown to be owned by Kentucky, because they “would have been paid to some agency_” McNally, 107 S.Ct. at 2882 (emphasis added). Thus, the money McNally kept was not owned by Kentucky once it was paid to the insurance agency. In contrast, the bribes Runnels kept are owned by Local 22, as we have shown in Section III. Even though Runnels argues that Shapero’s fees would have been paid in any event, the bribes would not have been.
The Supreme Court, in McNally, did not except from the scope of § 1341 a breach of fiduciary duty that causes a deprivation of an economic benefit, nor did it deny that a union or public official can be a fiduciary to those represented by the official. The Court did not address these issues. Rather, it noted that, as to McNally, “[t]he violation asserted [of the mail fraud statute] is the failure to disclose their financial interest, even if state law did not require it, to other persons in the state government whose actions could have been affected by the disclosure.” Id. at 2882 n. 9. The only fraud asserted was McNally’s failure to disclose information (which held no economic value). There was no deprivation of an economic benefit through a knowing violation of McNally’s fiduciary duty. Arguably, he also breached his fiduciary duty by his failure to disclose, but the Supreme Court has held that such a breach standing alone does not violate the mail fraud statute.
VI
Runnels argues that, because the workers’ compensation forms, which consti[1193]*1193tuted the “mail” portion of the fraud, were themselves legitimate and honestly prepared, the present case is governed by Parr v. United States, 363 U.S. 370, 80 5.Ct. 1171, 4 L.Ed.2d 1277 (1960). Parr required that where the government charged mail fraud in connection with the mailing of a tax return, the indictment had to specifically charge that the tax returns were themselves false and fraudulent.
The mailing in Parr was mandated by law. Whether there had been a fraud or not, the mailings would have occurred. In the current case, in contrast, had there been no agreement between Runnels and the law firms, it is all but certain that some of the mailings would not have occurred. Indeed, unless Runnels addressed the members, encouraging them to file claims, he did not receive payment. Of course, the material mailed need not itself be false if it aids in the execution of the fraud. United States v. Talbott, 590 F.2d 192 (6th Cir.1978); United States v. Reid, 533 F.2d 1255 (D.C.Cir.1976).
Runnels also argues that a plea bargain agreement between Shapero and the government, introduced into evidence by the government, was misleading because it represented that no charges against Shape-ro were being dropped. However, Runnels does not claim that he was harmed by any misrepresentation as to the agreement. Because Runnels has not shown any harm due to the introduction of the plea bargain, he is not entitled to relief.
C
On cross-examination, Runnels asked both Shapero and FBI agent Jay Sieger to reveal details about Shapero's fifteen-point plea bargain agreement with the government. The government’s objection on grounds of irrelevancy was sustained.6 Runnels contends that this made it impossible for him to show Shapero’s motive in testifying against him. Although Runnels was allowed to cover the issue generally, he argues that this did not permit the impact on the jury which would have resulted from showing Shapero’s reasons for cooperating with the government.
The record reveals that Runnels had ample opportunity to put evidence before the jury that there were allegations by many parties that Shapero had cheated, lied, and broken the law. Under Rule 403, Fed.R. Evid., it is a matter of the trial judge’s discretion as to whether evidence should be excluded as more prejudicial than probative. See United States v. Tracey, 675 F.2d 433, 439 (1st Cir.1982) (additional evidence redundant when jury has enough evidence to permit it to make a discriminating appraisal of witness’s motive); United States v. Renfro, 620 F.2d 497 (5th Cir.), cert. denied, 449 U.S. 921, 101 S.Ct. 321, 66 L.Ed.2d 149 (1980) (exclusion of evidence relevant to witness’s bias was held to be proper). Here, Runnels suffered little or no reduction in probative impact due to the exclusion of the details. We cannot say that the district judge exceeded the broad bounds of his discretion by this exclusion.
D
The government, by introducing Shapero’s plea of guilt into evidence, was attempting to mitigate the impression that his testimony was a wholly self-serving effort to fulfill his end of a bargain with the government. Runnels contends that it was improper to permit the introduction of the guilty plea, when a) that plea had not been accepted by the court to which it was submitted; b) that court had the option of refusing to accept the plea, which would permit Shapero to withdraw it; and c) Shapero had a deal with the government which permitted him to appeal his conviction on the count to which he had pled guilty, because the admission of the plea had an unfairly persuasive affect on the jury. This argument fails, however, because Runnels was permitted to cross-ex[1194]*1194amine Shapero on these very issues. Thus, the jury was informed of the actual state of affairs.
However, the government's tactic smacks of sharp practice, at the least. The only purpose in presenting Shapero’s guilty plea to the jury was to give the jury the impression that Shapero had no motive to be a favorable witness for the government. The judge’s decision admitting the guilty plea was therefore erroneous under Rule 403, Fed.R.Evid., as that evidence served no purpose other than to mislead the jury. However, the error was harmless, due to Runnels’s opportunity for cross-examination, which brought out the true role of the guilty plea. Fed.R.Crim.P. 52(a).
VII
Shapero’s only contention on appeal is that Runnels should not be criminally liable under § 1341 because that provision does not criminalize the fiduciary breach of a private party. Thus, Shapero argues, there was neither a cause of action against him nor a sufficient factual basis for his guilty plea. We have decided this question against Shapero’s contention in Section III of our opinion.
The decisions of the district court are AFFIRMED.