Opinion for the Court filed by Circuit Judge WALD.
WALD, Circuit Judge:These appeals are from the convictions of three individual defendants and a corporation on four counts of wire fraud, in violation of 18 U.S.C. § 1343 (1976), one count of transportation of the proceeds of fraud in interstate commerce, in violation of 18 U.S.C. § 2314 (1976), and one count of conspiracy, in violation of 18 U.S.C. § 371 (1976). The district court sentenced defendant Stephens to five concurrent five year prison terms and a suspended consecutive five year term, the suspension being *105conditioned on payment of $1 million restitution to Raytheon Company. It sentenced defendant Achuck to six suspended concurrent five year prison terms, suspension being conditioned on payment of $750,000 restitution to Raytheon. Defendant Lemire received six concurrent five year sentences. The three individual defendants were also fined $19,000 each, and defendant Interconex, Inc., was fined $24,000.
All four defendants challenge their convictions on the following grounds: (1) the district court misinstructed the jury on the requisite elements of wire fraud; (2) the instructions allowed the jury to convict on a theory of fraud different from that which the government presented at trial; (3) the district court erred in permitting the government’s use of a non-expert summary witness; and (4) the district court erred in not admitting three defense exhibits into evidence. In addition, Achuck challenges the sufficiency of the evidence to uphold his conviction. Finally, both Achuck and Stephens challenge the district court’s authority to set restitution as a condition of probation in this case. For the following reasons, we affirm the convictions and restitution conditions.
I. Background
The evidence in this case is both complex and controverted, but certain uncontested facts set the stage for analyzing the defendants’ appeals.
A. The Uncontested Facts
On June 16,1976, the Raytheon Company contracted with the Kingdom of Saudi Arabia to construct a complex missile system and military base. As part of that project, Raytheon decided to provide housing for its personnel in Saudi Arabia. At the time Raytheon entered this contract, and throughout the period involved in this case, Roy Carver was the program manager for the entire project, and Raytheon’s senior official in Saudi Arabia. Carver was involved in the alleged fraud and conspiracy but is not an appellant in this case. Defendant Joseph Lemire was the manager of several supporting subsidiaries of Raytheon and was responsible for procuring and shipping this housing to Saudi Arabia.
Prior to Raytheon entering the 1976 contract, Lemire and Carver became acquainted with defendants Jon Stephens and Lionel Achuck, who are co-owners of defendant Interconex, an international freight forwarder.1 Interconex had handled some of Raytheon’s previous shipping to Saudi Arabia. When Lemire began to seek bids for the housing project, however, Interconex no longer provided any shipping for Raytheon because Raytheon had entered an agreement with Waterman Steamship Line to handle its shipping needs.
At the time the alleged fraud occurred, Raytheon had a company-wide policy prohibiting employees from accepting anything of value from any organization that sought to or did provide goods or services for Raytheon. Every year, Lemire signed a card representing that he had complied with the conflict of interest policy. The policy also required Lemire to report any conflict of interest that arose after the card was signed. In addition, Raytheon had another company policy requiring that all companies making competing bids for contracts to provide Raytheon with goods or services be given the same bidding information at the same time.
In late May of 1976, Lemire had his staff member, Mr. Waxman, contact International Modular Systems, Ltd. (IMS), a District of Columbia company that produces modular homes. On June 7, Stephens met with the representatives of IMS to discuss their provision of houses to Saudi Arabia and, as a result of the meeting, Interconex and IMS signed an agreement that they would work together to get the Raytheon contract and to develop other business. That agreement provided that IMS would bid on the Raytheon contract, and, if successful, IMS *106would manufacture and deliver the prefabricated construction to port, and Interconex would ship and deliver the construction to the site in Saudi Arabia. On June 9, Le-mire spoke to IMS on the telephone and discussed modular housing for Saudi Arabia. On June 21, Mr. Waxman notified modular house manufacturers, including IMS, of the contract specifications; he told them that the bids were to include shipping and that the bids were due by June 23. Raytheon received four bids, of which the IMS bid was lowest. The bids differed greatly in their shipping charges, with IMS charging the least amount — in this case, $91.11 per ton.2 Lemire awarded the contract to IMS.
When the housing contract was let, Le-mire informed the Raytheon official responsible for approving procurement contracts that he had solicited bids C & F (cost and freight), that is, for both the housing and transportation. When questioned about his decision to have the manufacturers provide shipping, Lemire responded that the competitive bid for shipping would save Raytheon money. Raytheon’s management then approved the contract.
During this time, Achuck and Stephens made contractual arrangements allowing them to transfer funds into Winhall Insurance Company, a Bermuda based company in which each had a one-half interest. On June 10, they travelled to Geneva where Achuck obtained special power of attorney over a Liberian company, Generation Holding (GH), and Stephens obtained a similar power over Coralda Trust, Ltd., a company based in Lichtenstein. When IMS was awarded the Raytheon contract, it entered into a subcontract agreement with Interconex. Rather than have IMS pay Interconex the full $20.50 per square foot that the companies had agreed upon, IMS consented to pay $12.65 per square foot to Interconex and the remaining $7.85 per square foot to GH. When IMS was later awarded a second contract by Raytheon, it paid the same rate to Interconex, but paid $9.35 per square foot to GH. GH later funneled money to Coralda Trust which then transferred some of the funds to Winhall. In other transactions, GH transferred funds that ultimately ended up in a Cayman Island company owned by Carver and Lemire.
In the fall of 1976, Raytheon began an investigation of the IMS contracts, and in particular the shipping rates. In the course of this investigation, a company official asked Lemire about who arranged the shipping for IMS and Lemire responded that he did not know. Raytheon also asked IMS and Interconex for cost information about the shipping, and both refused to supply the information.3 Later in the fall, Raytheon got Interconex to cancel the fourth and final voyage upon which houses were being shipped. Raytheon itself chartered a boat to ship the houses, thereby achieving about $700,000 savings on the last trip. Tr. at 1148. Except for obtaining Interconex’s release from the shipping contract for the fourth voyage and arranging shipping for the houses itself, Raytheon took no further action. The government investigation leading to the indictment was prompted by surveillance of Mrs. Carver by a member of the Saudi Royal family. The grand jury indicted the defendants and Mr. Carver on September 11, 1981.4
B. The Parties’ Theories of the Case
At trial, the government focused its proof primarily on its allegation that Interconex overcharged Raytheon for shipping. The government’s theory was that Interconex was able to submit a lower bid than its *107competitors because of contract specification information that Lemire provided it well in advance of the bidding.5 This information enabled Interconex to calculate its rate based on knowledge that it could charter an entire vessel to ship the housing, rather than booking shipments with a common carrier. The government contended that this knowledge allowed Interconex to achieve inflated profits while still submitting the lowest bid. These excess profits were then divided among Carver, Lemire, Stephens and Achuck. It also argued that even if Interconex’s shipping rate was not inflated in comparison to other bids and the Waterman Steamship rate, the scheme prevented Raytheon from saving money by chartering a boat itself, for the first three voyages. The government claims that Raytheon’s agreement with Waterman was not an exclusive contract and covered small shipments only; thus it did not preclude Raytheon from chartering its own boat.
The defense denied that Lemire gave Interconex any advance information. It claimed that had Lemire not included shipping as part of the contract, Raytheon would have paid $164.50 per ton for shipping at the Waterman rate. Thus, Lemire was acting in Raytheon’s best interest in including the shipping as part of the housing contract and in awarding the contract to IMS. Moreover, the defense argued that Lemire did not deny Raytheon the opportunity to charter its own boat. Lemire testified that he would never have considered chartering a vessel because he was not free to make such arrangements, believing he had to use Waterman. He pointed out that Raytheon had never before chartered its own boat.
The defense explained the transfer of funds from GH to Carver and Lemire as independent of the award of the IMS contract. Lemire testified that he did not know that GH was the source of the funds, and in fact that he did not know of GH’s existence until the government investigation preceding the indictment. The defense contended that the funds were Stephen’s and Achuck’s capital investment for an independent joint venture by Carver, Lemire, Stephens and Achuck to build a modular housing factory in Saudi Arabia. Thus, Le-mire denies having gotten a kickback from Interconex for aiding them in getting the shipping contract.
II. Instructions on Wire Fraud
The defendants contend on appeal that the instructions to the jury incorrectly stated the law on the essential elements of wire fraud. They assert that the instructions erroneously allowed the jury to convict based on a theory that Lemire’s and Carver’s failures to disclose their conflicts of interest due to their alleged joint venture with Stephens and Achuck, without more, constituted a material non-disclosure evidencing a specific intent to defraud Raytheon. The government responds that the instructions were entirely correct, i.e., that a failure to disclose a conflict of interest, when accompanied by a specific intent to defraud the employer of the undisputed loyalty of his employees, is sufficient to support a wire fraud conviction. Thus, it claims that even under the defendants’ version of the facts, the jury could have convicted the defendants for defrauding Raytheon of the loyal and honest services of its employees Lemire and Carver. Although we agree with the defendants that the government’s interpretation of the wire fraud statute encompasses too much, we find that a fair reading of the instructions in light of the evidence and arguments the jury heard, does not support an inference that the jury acted pursuant to such an impermissibly broad interpretation of the statute.
A. The Scope of Criminal Fraud
The elements of wire fraud are (1) formation of a “scheme to defraud,”6 and *108(2) use of interstate wire communication to further that scheme.7 See United States v. Pollack, 534 F.2d 964, 971 (D.C.Cir.), cert. denied, 429 U.S. 924, 97 S.Ct. 324, 50 L.Ed.2d 292 (1976); cf. Pereira v. United States, 347 U.S. 1, 8, 74 S.Ct. 358, 362, 98 L.Ed. 435 (1954) (elements of mail fraud); United States v. Diggs, 613 F.2d 988, 997 (D.C.Cir.1979) (same); United States v. George, 477 F.2d 508, 511 (7th Cir.) (same), cert. denied, 414 U.S. 827, 94 S.Ct. 155, 38 L.Ed.2d 61 (1973). Congress did not define “scheme or artifice to defraud” when it first coined that phrase, nor has it since. See United States v. Reid, 533 F.2d 1255, 1264 (D.C.Cir.1976); United States v. Von Barta, 635 F.2d 999, 1005 (2d Cir.1980), cert. denied, 450 U.S. 998, 101 S.Ct. 1703, 68 L.Ed.2d 199 (1981).8 Instead that expression has taken on its present meaning from 111 years of case law.9 See Von Barta, 635 F.2d at 1005 (legislative history helpful); United States v. McNeive, 536 F.2d 1245, 1247 n. 3 (8th Cir.1976) (same).
At the core of the judicially defined “scheme to defraud” is the notion of a trust owed to another and a subsequent breach of that trust. But “[n]ot every breach of a fiduciary duty works a criminal fraud.” George, 477 F.2d at 508. In their attempts to delineate which breaches of duty rise to the level of criminal fraud, courts have used various limiting doctrines. Some, including this court, have required that the fraud be “active” — that the fiduciary utilize his trusted position to obtain a benefit for himself at the expense of the person whose trust he breaches. See Post v. United States, 407 F.2d 319, 329 (D.C.Cir.1968), cert. denied, 393 U.S. 1092, 89 S.Ct. 863, 21 L.Ed.2d 784 (1969); Epstein v. United States, 174 F.2d 754, 766 (6th Cir.1949). Other courts have required that the breach be accompanied by some material non-disclosure or misrepresentation to the party owed the duty. See, e.g., United States v. Ballard, 663 F.2d 534 (5th Cir. Unit B 1981), modified in part and reh’g denied, 680 F.2d 352 (5th Cir. Unit B 1982); Von Barta, 635 F.2d at 1006. The crux of these requirements is that the wire fraud statute makes criminal only breaches of duty that are accompanied by a misrepresentation or nondisclosure that is intended or is contemplated to deprive the person to whom the duty is owed of some legally significant benefit. See Diggs, 613 F.2d at 997 (“proof of fraudulent intent is critical”); Ballard, 663 F.2d at 541 n. 17 (relating materiality to active fraud).
Although critical ambiguities about the scope of the wire fraud statute remain, there is judicial consensus about certain requisite elements of a scheme to defraud. The duty breached need not arise *109from state or federal law; in particular, it may stem from an employment relationship of the sort that imposes discretion and consequently obligations of loyalty and fidelity on the employee. See, e.g., Ballard, 663 F.2d at 541; Von Barta, 635 F.2d at 999; United States v. Bohonus, 628 F.2d 1167, 1172 (9th Cir.), cert. denied, 447 U.S. 928, 100 S.Ct. 3026, 65 L.Ed.2d 1122 (1980); United States v. Reece, 614 F.2d 1259, 1261 (10th Cir.1980); United States v. Bryza, 522 F.2d 414, 422 (7th Cir.1975), cert. denied, 426 U.S. 912, 96 S.Ct. 2237, 48 L.Ed.2d 837 (1976). And although the scheme to defraud must threaten some cognizable harm to its target, that harm need not be a deprivation of tangible property or money; criminal fraud encompasses schemes to defraud persons of significant intangibles as well. See, e.g., United States v. Condolon, 600 F.2d 7, 8 (7th Cir.1979) (scheme to obtain sexual favors by false promises of modelling or acting job); United States v. Louderman, 576 F.2d 1383, 1387-88 (9th Cir.) (scheme to invade privacy by obtaining confidential information from telephone company), cert. denied, 439 U.S. 896, 99 S.Ct. 257, 58 L.Ed.2d 243 (1978). With the broadening of the scope of the statute to cover intangible harms, however, has come a certain amount of confusion and controversy over the outer boundaries of wire fraud. In particular, premising a felony solely on a scheme to defraud an employer of the loyal services of his employee has spawned a fierce debate about potential over-criminalization of employer-employee breakdowns, better handled in the civil courts.10 Carried to its logical extreme, such a theory would criminalize any intentional undisclosed breach of duty to an employer. The government appears to be arguing just such a theory here, but we are not inclined to accept it for the following reasons.
An employer values the loyalty of his employees and prohibits conflicts of interest primarily because such conflicts create an incentive for the employee to act in a manner detrimental to the employer’s tangible monetary interests. Employee loyalty is not an end in itself, it is a means to obtain and preserve pecuniary benefits for the employer. An employee’s undisclosed conflict of interest does not by itself necessarily pose the threat of economic harm to the employer. Therefore it does not alone constitute a sufficient indicium that the employee intended any criminally cognizable harm to the employer.11 Other sur*110rounding circumstances may of course provide the necessary proof that the employee intended such harm.12 We hold today, however, that an intentional failure to disclose a conflict of interest, without more, is not sufficient evidence of the intent to defraud an employer necessary under the wire fraud statute.13 See United States v. Feldman, 711 F.2d 758, 763 (7th Cir.1983). There must be a failure to disclose something which in the knowledge or contemplation of the employee poses an independent business risk to the employer. Other courts have so held. Von Barta, 635 F.2d at 1005 n. 14; United States v. Dixon, 536 F.2d 1388, 1400-01 (2d Cir.1976).
At the same time, we are not unaware that undisclosed conflicts of interest create fertile ground for subsequent misuse of the employee’s position. “The vice against which [courts] seek to guard ... is that the adverse interest of the individuals may overcome [their] duty [as] officials, and induce agreements and transactions detrimental to the [employer] and unduly beneficial to the individuals.” Epstein, 174 F.2d at 764, (quoting Wyman v. Bowman, 127 F. 257, 273 (8th Cir.1904)). Accordingly, our holding does not remove from the ambit of wire fraud undisclosed conflicts that, accompanied by activity on the part of the employee, carry a significant risk of identifiable harm to the employer apart from the loss of his employee’s loyalty and fidelity. So long as the jury finds the non-disclosure furthers a scheme to abuse the trust of an employer in a manner that makes an identifiable harm to him, apart from the breach itself, reasonably foreseeable, it may convict the employee of wire fraud. The crucial determination must be whether the jury could infer that the defendant might reasonably have contemplated some concrete business harm to his employer stemming from his failure to disclose the conflict along with any other information relevant to the transaction. See Von Barta, 635 F.2d at 1005 n. 14; Dixon, 536 F.2d at 1399 n. 11.
Although this formulation may differ in some respects from that of other courts, we believe it only makes more explicit what they meant by a “material non-disclosure or misrepresentation.”14 The leading case defining “material non-disclosure” is Ballard, 663 F.2d 534, which involved a scheme to channel oil through a chain of oil companies in order to generate commissions. The *111scheme’s mastermind, Mr. Granlund, was hired by the Florida Power Company to obtain oil during the 1973 oil shortage. The Florida Power Company paid him for this and also allowed him to receive commissions from the oil companies. By channelling the purchases through five companies, Granlund received five commissions on each sale; channelling in turn was arranged by giving kickbacks to employees of the intermediary companies responsible for purchases and sales of oil. The intermediaries were subject to price controls which limited the profit they could make on sales of oil. The Ballard court held that in light of these price controls the employees of the intermediaries did not intend to defraud their employers because the employers already received the maximum profits on each sale. The court reasoned that the failure of the employees to disclose the scheme to the intermediary employers would therefore not have altered their business conduct, so the non-disclosure was not material.15
In Ballard, the Fifth Circuit stated that a non-disclosure is material only if the employee “has reason to believe that the information would lead a reasonable employer to change its business conduct.” 663 F.2d at 541; see also Feldman, 711 F.2d at 763 (simple concealment of conflict of interest in customer’s accounts immaterial because it would not itself have enabled defendant to trade without advancing sufficient collateral); United States v. Bethea, 672 F.2d 407 (5th Cir. Unit B 1982) (procurement officer’s ordering storage for servicemen who did not request it, thereby giving business to cosigner of defendant’s loan, not fraud unless activities were not in furtherance of servicemen’s best interest). Since an employer presumably would “change its business conduct” only if, upon disclosure of the conflict and any other relevant information, it saw new opportunities for profit or savings, or dangers of economic harm, the notion of materiality of non-disclosure or misrepresentation in the wire fraud context must logically focus on the reasonable foreseeability by the employee of potential economic harm to his employer stemming from the employer’s ignorance of information relevant to the conflict.
B. The Jury Instructions
Under our standard for wire fraud, the jury would have had to find that the defendants’ failure to disclose Lemire’s and Carver’s conflicts of interests were in furtherance of a scheme to defraud Raytheon of a business opportunity or economic benefit. If the jury believed the government’s evidence that the defendants schemed to overcharge Raytheon for shipping in order to channel excess profits into their own venture, it could properly convict. The jury could also properly have found them guilty if it believed Lemire or Carver knew of Interconex’s plan to charter an entire boat to ship the housing and did not inform Raytheon of this money-saving option, thereby depriving Raytheon of the opportunity to arrange its own shipping — assuming, of course, that Lemire did not sincerely believe Raytheon could not charter a boat itself because of its Waterman commitment. Or, if the jury found that Lemire had solicited bids for modular housing C & F or had otherwise altered the standard procedure for letting the contract in order to enable Interconex to get the shipping contract to the detriment of Raytheon’s best interests, then it might justifiably convict the defendants of wire fraud. If the jury, however, found only an undisclosed breach of fiduciary duty on Lemire’s and Carver’s part due to their interest in a joint venture with Interconex’s principals, then it could not properly convict because there was nothing inherent in that failure to dis*112close that spelled business loss or harm to Raytheon.
We turn then to the trial judge’s instructions to see if they could reasonably be interpreted by the jury to allow a conviction of wire fraud upon a mere finding of failure to disclose Lemire’s and Carver’s conflict of interest stemming from the joint venture. If in light of all the circumstances — the language of the instructions, the arguments of counsel, and the evidence itself — we find that the jury may have convicted the defendants solely upon that undisclosed conflict, those convictions must be reversed. See, e.g., Ballard, 663 F.2d at 544 (reversing and remanding because “the jury was authorized to find [defendant] guilty if the government made out facts supporting any of the criminal theories embodied in the [district] court’s charge to them,” including those rejected by the court of appeals). Alternatively, if these factors cumulatively indicate that it is highly improbable that the jury found the defendants guilty under an improper legal theory, technical errors in the instructions are deemed harmless, and we will affirm. See Alexander v. United States, 418 F.2d 1203 (D.C.Cir.1969) (error in instructions harmless if all that happened at trial gave fair assurance that the jury was not substantially swayed by error); United States v. Herbert, 698 F.2d 981, 986-87 (9th Cir.1983) (in light of evidence, no reasonable possibility that error had materially affected verdict); United States v. Brooklier, 685 F.2d 1208 (9th Cir.1982) (insufficient evidence of extortion meant that charge dealing with extortion on RICO count was erroneous, but error “harmless beyond reasonable doubt” since prosecutor told jury that defendants were not involved in the extortion and not to consider extortion in assessing guilt or innocence under RICO), cert. denied, 459 U.S. 1206, 103 S.Ct. 1194, 75 L.Ed.2d 439 (1983); United States v. Pine, 609 F.2d 106, 108 (3d Cir. 1979) (proper test is to determine improper instructions’ effect on jury’s understanding of the law).16
The defendants mainly challenge the portions of the charge that address the legal requirements of a “scheme or artifice to defraud.” In stating those requirements, the judge instructed:
the first alleged object was to defraud Raytheon Company of its right to the honest, conscientious, faithful, loyal, disinterested and unbiased services, actions, and performances of duties by its employees Carver and Lemire, free from bribery, corruption, partiality, willful omission, bias, dishonesty, deceit, misconduct and fraud.
Now the object of the scheme need not be money or any form of tangible property. The government need not prove any actual loss of money by the Raytheon Company.
A scheme to defraud an employer of the honest, faithful and unbiased services of its employees can also come within the meaning of scheme or artifice to defraud as set forth in the wire fraud statute.
Tr. at 3175-76. By themselves, these words are ambiguous; conceivably they could be interpreted to allow a conviction solely on *113the basis of a knowing failure to disclose a conflict of interest, such as Lemire’s interest in the joint venture with the principals of Interconex.
The remainder of the instructions, however, lead us to conclude that the jury was unlikely to have convicted for a mere failure to disclose such a conflict of interest. We must look at the jury instructions as a whole in assessing whether they constituted prejudicial error. United States v. Park, 421 U.S. 658, 674-75, 95 S.Ct. 1903, 1912-13, 44 L.Ed.2d 489 (1975); United States v. Baker, 693 F.2d 183 (D.C.Cir.1982); Pollack, 534 F.2d at 973; United States v. Martin, 475 F.2d 943, 947 (D.C.Cir.1973).17 The instructions immediately following the troublesome language confirmed the admonition that both a breach of fiduciary duty and material non-disclosure were required by the statute.18 The instructions were thus technically correct because they prefaced the non-disclosure requirement by the word “material,” which under our legal standard requires that the employee reasonably contemplate the risk of some lost business opportunity or more direct pecuniary harm to the employer resulting from the non-disclosure. See Bethea, 672 F.2d at 414; Ballard, 663 F.2d at 541. Of course, as we noted at argument, one can hardly expect lay jurors to recognize nice legal concepts embedded in the definition of materiality,19 especially when, as in this case, the *114lawyers and the court do not themselves agree on the precise content of that definition.20 But there was an additional statement in the instructions that, “although the government need not show that the alleged victims were in fact defrauded, the government must prove beyond a reasonable doubt that some actual harm or injury was at least contemplated.” Tr. at 2876. Although this statement may appear mainly to address the issue of whether the jury could convict even if it found the scheme was unsuccessful, see United States v. Schaeffer, 599 F.2d 678 (5th Cir.1979) (refusing defendant’s proposed instruction that the governmént must show that someone was defrauded since success of scheme was not required); United States v. Reid, 533 F.2d at 1261-62 (not necessary to show victim actually incurred loss), the emphasis on “actual harm” (emphasis supplied) projects to the layman a requirement that there be a threat of monetary loss.
Later instructions on specific intent also helped to cure any defect in the instructions on “scheme to defraud.” There the district court did focus the jury’s attention on the need to find that the defendants contemplated some kind of pecuniary harm to the employer. It defined “intent to defraud” as follows:
Now, to act with intent to defraud means to act wilfully and with specific intent to deceive or cheat, ordinarily for the purpose of either causing some financial loss to another or bringing about some financial gain to one’s self.
Tr. at 3209-10 (emphasis supplied). Although the emphasis on financial loss and benefit is weakened somewhat by the fact that this instruction appears thirty-two pages after the challenged portion defining “scheme to' defraud,” the district court specifically connected up this definition of “intent to defraud” with the prior instructions on the wire fraud counts.21 Thus, a conscientious and attentive juror viewing the instructions as a whole, would have hesitated to convict on the wire fraud counts without finding that the defendants did something to show they intended to take a financial or business advantage of Raytheon.22
Moreover, although the central instruction on “scheme to defraud” failed to define a legally significant term like “material non-disclosure,” and the curing instruction on specific intent came much later in the charge, we do not believe the instructions were significantly confusing for another reason. In the context of this trial, and in light of the actual evidence and arguments presented to the jury we think it extremely unlikely that the jury was misled into thinking that the mere failure to disclose Lemire’s and Carver’s conflicts of interest without any other action on their part against Raytheon’s business interests was sufficient to constitute wire fraud. As the defense itself noted, “[t]he evidence introduced by the government during the trial focused on ... alleged excessive charges.” Brief for Appellants at 27. And the government’s closing argument mentioned *115Lemire’s failure to disclose a conflict of interest only as part of a scheme to hurt Raytheon financially either by overcharging or denying Raytheon the opportunity to ship goods more cheaply.23 In sum, the jurors would have had to shift from consideration of -the major thrust of the government’s evidence and arguments and dwell on a few ambiguous lines in an eighty-six page charge in order to convict on an improper theory.
The verdict itself also suggests that the jury did not in fact base its conviction solely on the existence and non-disclosure of Le-mire’s and Carver’s conflicts of interest. The jury convicted all the defendants of count two, interstate transportation of a security taken by fraud. In order to do so, under the statute and under the instructions, not challenged here, it must have determined that a $775,008 check paid to Generation Holding was “stolen, converted or taken by fraud.” Tr. 3182. The evidence presented identified no means by which that check could have been “taken by fraud” other than by the defendants’ fraudulent scheme. To have found that the check was “taken by fraud,” the jury would at least have had to conclude that the shipping contract for which the check was payment would not have been consummated but for the fraud. This conclusion would not follow from a finding of a mere failure to disclose a theoretical conflict of interest; *116the jury must have found that the fraud affected how Raytheon shipped the modular housing. The conviction on count two thus carries a necessary implication that the jury actually did find that the defendants defrauded Raytheon of at least $775,008. Hence it is reasonable to assume that the conviction on the mail fraud counts was based on the same finding that a scheme existed to defraud Raytheon of that money.
Even were we less certain that the offending language of the instructions did not control the verdict, we would still hesitate to reverse. To the extent the instructions were confusing and even misleading, the defense had ample opportunity to make clarifying suggestions. Rule 30 of the Federal Rules of Criminal Procedure states:
No party may assign as error any portion of the charge or omission herefrom unless he objects thereto before the jury retires to consider its verdict, stating distinctly the matter to which he objects and the grounds for his objection.
(Emphasis supplied.) “The rule requires that illegal errors in jury instructions be brought to the attention of the trial judge in order to provide an opportunity for their immediate correction.” United States v. Campbell, 684 F.2d 141, 148 (D.C.Cir.1982); United States v. Williams, 521 F.2d 950, 956 (D.C.Cir.1975). At the pre-charge conference, the defendants did object that the instruction on “scheme to defraud” was confusing, Tr. at 2879, but the trial judge incorporated the bulk of their suggested revisions.24 Tr. at 2284-87. Following this incorporation, of which the judge notified counsel at the pre-charge conference, the defendants did not apprise the district court of any remaining dissatisfaction with the language of this instruction. We are consequently less receptive to their complaint on appeal that the language they reviewed in detail at trial was incorrect or misleading.25
We emphasize at this point that if we believed there was a substantial possibility that the jury convicted on an improper legal theory, we would be inclined toward a liberal construction of the defendants’ obvious dissatisfaction with the instruction on alternative objects of the “scheme to defraud,” even though their objection was based on grounds of surprise and variance rather than legal insufficiency. But we find no such significant likelihood here.
C. Alleged Variance in the Theory of the Case
The defendants mainly attack the instructions on the ground that they changed the theory of the case from that charged by *117the indictment. They characterize as a “key element of the government’s theory” in the indictment and at trial, alleged inflated shipping rates that Interconex charged Raytheon. Brief for Appellants at 22. They say the indictment alleged a scheme to defraud with a single object — to obtain $2.1 million in excess profits by using Lemire and Carver as disloyal intermediaries in the contracting process. Id. at 22-23. The defendants thus claim that the instruction allowing the jury to convict solely for fraudulent deprivation of Raytheon’s employees’ honest and loyal services changed the basic elements of the crime from the indictment. They further support this claim by noting a small, but in their view fundamental, word difference between the government’s initial jury instructions, proposed before the trial, and the government’s final instructions, proposed after the defense presented its case. The initial instruction on the elements of wire fraud read:
The government must prove that ... the defendants devised ... a scheme or artifice to defraud ... with the following objects: (1) ... to defraud the Raytheon Company of its right to the honest, ... loyal ... services ... of its employees ...; (2) ... to obtain money from the Raytheon Company by means of false pretenses.
J.A. 374. Over the defense counsel’s vehement objection, the final instructions substituted “with one or both of the two following objects” for “with the following objects.” Tr. at 2866-76 (emphasis supplied). The defendants argue that the modified jury instructions indicated that the government abandoned its original theory premised on inflating shipping charges midstream for a broader one premised on general disloyalty through undisclosed conflicts. Brief for Appellant at 29, 31-32.
We note at the outset that “proof at trial need not, indeed cannot, be a precise replica of the charges contained in the indictment.” United States v. Heimann, 705 F.2d 662 (2d Cir.1983). Since the instructions tell the jury how the law relates to the facts, they too will deviate somewhat from the indictment. The real issue is not whether the instructions vary from the indictment, but how far they may vary before the variance infringes on the defendant’s rights. See Berger v. United States, 295 U.S. 78, 82, 55 S.Ct. 629, 630, 79 L.Ed. 1314 (1935); United States v. Mangieri, 694 F.2d 1270, 1278 (D.C.Cir.1982); United States v. Jordan, 626 F.2d 928, 931 (D.C.Cir.1980) (per curiam). A substantial deviation of instructions from an indictment is impermissible because first it requires a defendant to answer a criminal charge that was not brought by a grand jury, see Russell v. United States, 369 U.S. 749, 82 S.Ct. 1038, 8 L.Ed.2d 240 (1962) (bill of particulars does not preserve defendant’s right to be tried on a charge framed by a grand jury); Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960); Gaither v. United States, 413 F.2d 1061, 1066 (D.C.Cir.1969), and second it denies the defendant sufficient notice to prepare and present an adequate defense.26 See Berger, 295 U.S. at 81-82, 55 S.Ct. at 630; United States v. Goss, 650 F.2d 1336, 1346 n. 11 (5th Cir.1981); United States v. Smolar, 557 F.2d 13, 19 (1st Cir.), cert. denied, 434 U.S. 866, 966, 971, 98 S.Ct. 203, 508, 523, 54 L.Ed.2d 143, 453, 461 (1977); cf. Pollack, 534 F.2d at 970 (indictment sufficient because it outlined mail and wire fraud scheme with sufficient particularity to avoid surprise and permit defendants to prepare a defense). We believe, however, that the defendants here were denied neither right.
*118The defendant is deprived of his right to have all charges screened by the grand jury only if the deviation in proof or instructions from the specifics of the indictment affects an essential element of the offense charged. See Mangieri, 694 F.2d at 1277-78; Gaither, 413 F.2d at 1071; United States v. Gonzales, 661 F.2d 488, 492 (5th Cir.1981). Here the challenged instructions did not deviate from the indictment regarding any element of wire fraud.27 The indictment alleged that the defendants devised a scheme to defraud Raytheon of its right to Carver’s and Lemire’s loyal services, and to obtain money from Raytheon by false pretenses.28 The correct method of pleading alternative means of committing a single crime is to allege the means in the conjunctive. See Joyce v. United States, 454 F.2d 971, 976 (D.C.Cir.1971), cert. denied, 405 U.S. 969, 92 S.Ct. 1188, 31 L.Ed.2d 242 (1972); Morrison v. United States, 365 F.2d 521, 522-23 (D.C.Cir.1966); United States v. Hicks, 619 F.2d 752, 758 (8th Cir. 1980). Hence, the opposed instruction merely makes explicit that either object of the scheme was sufficient.
A variance that does not alter an essential element of the charge may still deprive the defendant of an opportunity to meet the prosecutor’s case. Berger, 295 U.S. at 82, 55 S.Ct. at 630; Mangieri, 694 F.2d at 1277; Gaither, 413 F.2d at 1071. But here the indictment gave warning that the government might argue for a verdict based on deprivation of employee loyalty. In addition, its proposed instructions before the trial repeated that theory.
The object of the scheme need not be money or any form of tangible property. A scheme to defraud an employer of the honest, faithful and unbiased services of its employees can come within the meaning of “scheme or artifice to defraud” as set forth in the wire fraud statute.
J.A. at 233. Even if the indictment was ambiguous, this instruction clearly put the defendants on notice that the government did not believe its case hinged solely on proof of inflated shipping charges.29
The defense cites Smolar, 557 F.2d 13, and United States v. San Juan, 545 F.2d 314 (2d Cir.1976) as “[t]he applicable cases” holding “that the government may not change the theory of the case after the evidence has been closed.” Reply Brief for Appellants at 10. Smolar, however, involved a change of the theory of the case from “outright fraud as charged in the indictment, [to] a breach of fiduciary duty.” Smolar, 557 F.2d at 18. In this case, what happened was very different — at the end of trial the government reasserted a legal theory of the case set out in the indictment. San Juan involved a violation for bringing more than $5000 into the country without filing a customs report. The defendant failed to file a report on the bus on which she entered the country, and refused to file the report minutes later in the customs *119house. The government explicitly and repeatedly assured the court, the jury, and the defense counsel that it was not charging a crime for refusal to file the report in the customs house. 545 F.2d at 319 & n. 13. The government changed its theory of the case on appeal, after it appeared that the jury had convicted the defendant of failing to file a report on the bus without substantial evidence of wilfulness. Furthermore, the government’s assurances had precluded the court from considering the defendant’s motion to dismiss the charge because she could not have committed the crime in the customs house. Nothing of that sort ensued here. Hence, we do not find Smolar and San Juan dispositive of the issue before us.
In sum, the instructions given by the district court did not materially deviate from the indictment. The instructions neither charged the defendants with an offense different from that charged by the grand jury, nor deprived the defendants of an opportunity to present their full defense to the original charges. The more serious question, however, is whether an indictment and instructions based on two alternative theories of guilt, one of which may not correctly reflect our interpretation of the law, can lay a sound basis for a conviction. We have discussed that dilemma, in the context of this case, at length, supra, at 1338-1343, and concluded that the way in which the government tried the case as well as the overall thrust of the instructions, sufficiently diluted the effects of the flawed parts of the indictment and instructions. In short, the core of the defendants’ most persuasive challenge, which we have rejected, must be the possibility they were convicted under a wrong theory of law, not the technical defense that they suffered from surprise due to variance of the instructions from the indictment.
As we view the case, the government alleged one valid and one possibly invalid theory of guilt, concentrated its proof on the valid theory, and reincarnated the invalid one at the conclusion of the trial in its requests for instructions (unfortunately accepted). The net result was that the jury, sitting through a twenty-nine day trial, heard a snippet of the invalid theory at the beginning, a paragraph or two in an eighty-six page charge at the end, and in between a concentration of proof that there was a scheme to defraud Raytheon through diversion of profits from a specially concocted deal.
We suspect that the astute defense counsel knew, or should have known, from the indictment what the government’s ultimate legal position was. That ultimate theory has been the subject of much comment and controversy for several years. The defense may have been relieved when the proof and argument focused on actual money loss, rather than mere breach of fiduciary duty. And when the government resurrected its present theory of breach of fiduciary duty at the end of trial, the defense understandably objected, but its objection should have been on legal — not variance — grounds. Accordingly, we reject the defense argument for reversal based on prejudicial surprise and variance.
III. Evidentiary Rulings
A. The Summary Witness
Toward the end of its case-in-chief the government requested that the court allow James Kasper, an FBI agent and certified public accountant, to summarize the evidence about the complex cash flow through offshore companies that the government had introduced via direct examination of its witnesses. Kasper used four summary charts to re-examine this evidence in a more organized fashion. He relied on numerous letters, invoices and bank drafts, as well as the testimony of numerous witnesses already in evidence to present his summary. Kasper prefaced each piece of his testimony by identifying the document in evidence from which he obtained the information. The defendants objected to Kasper’s testimony on the grounds that he was an improper witness under the Federal Rules of Evidence, and his testimony would unfairly prejudice their defense. The district court held a full voir dire examination *120before ruling that Kasper would be allowed to testify, subject to limiting instructions that his testimony was explanatory and was not itself substantive evidence. The defendants renew on appeal objections rejected by the district court.
They argue that a non-expert summary witness is improper under Federal Rule of Evidence 602. Rule 602 requires that non-experts testify only as to matters of which they have personal knowledge;30 its purpose is to assure reliability. See Fed. R.Evid. 602 advisory committee note. In this case, neither Rule 602’s literal language nor its overriding purpose was violated. Kasper did not testify about any of the events underlying the trial: he only summarized evidence about cash flows that several prior witnesses had already offered. As to that evidence, he testified from his personal knowledge of the transcripts and exhibits. Hence Rule 602 does not bar his testimony.
This court has not previously ruled on the admissibility of one witness’s summary of evidence already presented by prior witnesses. Other courts, however, have recently confronted the question and permitted such summaries under Rule 1006, allowing for admission into evidence of summaries of documents too voluminous to be conveniently examined in court. See, e.g., United States v. Atchley, 699 F.2d 1055 (11th Cir.1983); United States v. Scales, 594 F.2d 558 (6th Cir.), cert. denied, 441 U.S. 946, 99 S.Ct. 2168, 60 L.Ed.2d 1049 (1979); United States v. Evans, 572 F.2d 455 (5th Cir.), cert. denied, 439 U.S. 870, 99 S.Ct. 200, 58 L.Ed.2d 182 (1978); United States v. Nathan, 536 F.2d 988, 996 (2d Cir.), cert. denied, 429 U.S. 930, 97 S.Ct. 337, 50 L.Ed.2d 300 (1976). The defendants argue that Rule 1006 was meant to be restricted to summaries of writings not feasible for direct admission into evidence. See Reply Brief for Appellants at 24. The language of Rule 1006, however, supports a broader interpretation that would allow summaries of documents already in evidence.31 The mere fact that the documents at issue are already in evidence assures neither that they can be “conveniently examined in court” nor that they have been examined in court. In this case, Judge Johnson explicitly noted that she was “unable to permit in court examination of each [document] by the jury.” Tr. at 2016. In any case, we note that Rule 1006 was designed primarily as an exception to the best evidence rule, see United States v. Johnson, 594 F.2d 1253, 1255 (9th Cir.), cert. denied, 444 U.S. 964, 100 S.Ct. 451, 62 L.Ed.2d 376 (1979), and since the evidence itself here was already before the court, there is no issue of inadmissibility under Rule 1002 as a replacement for the “best evidence.” See S. Saltzburg & K. Redden, Federal Rules of Evidence Manual 751 (3d ed. 1982). Hence, “[ejntirely aside from Rule 1006, there would still be ample authority for the admission of [summary testimony] into evidence. ... There is an established tradition that permits a summary of evidence to be put before the jury with proper limiting instructions.” Scales, 594 F.2d at 563; see, e.g., United States v. Esser, 520 F.2d 213, 218 (7th Cir.1975), cert. denied, 426 U.S. 947, 96 S.Ct. 3166, 49 L.Ed.2d 1184 (1976); Gordon v. United States, 438 F.2d 858 (5th Cir.), cert. denied, 404 U.S. 828, 92 S.Ct. 139, 30 L.Ed.2d 56 (1971). Thus, we conclude that the Federal Rules of Evidence do not bar use of non-expert summary testimony such as is presented in this case.
The contention that Kasper’s testimony unfairly prejudiced the defendants raises *121more troubling concerns, heightened by the fact acknowledged by Judge Johnson that the non-expert summary evidence was cumulative, and hence subject to challenge under Rule 403. See Tr. at 1930; S. Saltzburg & K. Redden, supra, at 751 (“summaries of documents introduced in evidence ... are better handled under Rule 403” than under Rule 1006); cf. Zenith Radio Corp. v. Matsushita Electrical Industrial Co., 505 F.Supp. 1313, 1334 (E.D.Pa.1980) (as amended 1981) (expert opinions that merely rehash evidence inadmissible because unhelpful). Since the summary testimony is relevant, under Rule 403 it is admissible unless the dangers of unfair prejudice it creates outweigh its probative value. See United States v. Burkley, 591 F.2d 903 (D.C.Cir.1978), cert. denied, 440 U.S. 966, 99 S.Ct. 1516, 59 L.Ed.2d 782 (1979); United States v. Day, 591 F.2d 861 (D.C.Cir.1978). Unlike the probative value of expert testimony, which can “instruct the court in the ways of [the expert’s] work,” Zenith Radio, 505 F.Supp. at 1334, the value of a summary witness is more subtle. But, just as an expert can assist a jury by imparting special knowledge that helps the jury to understand technical evidence, a non-expert summary witness can help the jury organize and evaluate evidence which is factually complex and fragmentally revealed in the testimony of a multitude of witnesses throughout the trial. See Scales, 594 F.2d at 563 (purpose of summary witness is simply to aid the jury in examination of evidence already admitted).
Nonetheless, there are obvious dangers posed by summarization of evidence. United States v. Apodaca, 666 F.2d 89 (5th Cir.), cert. denied, 459 U.S. 823, 103 S.Ct. 53, 74 L.Ed.2d 58 (1982). Although we usually defer to the district court’s assessment of whether the probative value of evidence outweighs the possibility of prejudice, see United States v. Wright, 489 F.2d 1181, 1186 (D.C.Cir.1973) (standard of review is abuse of discretion); United States v. Dennis, 625 F.2d 782 (8th Cir.1980), the pervasiveness of these dangers requires that we review the use of a summary witness closely-
One danger is that a jury will treat the summary as additional evidence or as corroborative of the truth of the underlying testimony. “This danger has led to the requirement of ‘guarding instructions’ to the effect that the [summary] is not itself evidence but is only an aid in evaluating evidence. Even with such instructions, a summary may be considered too conclusory, or as emphasizing too much certain portions of the Government’s case, or as presenting incompetent facts.” Scales, 594 F.2d at 564. In this case, however, we think the dangers are shadow, not substance. The trial judge gave the requisite guarding instructions32 and, through voir dire examination, allowed the defense to object to any portions of the summary testimony before the jury heard them. This device minimized substantially the danger that the jury might treat the summary as substantive evidence. See Scales, 594 F.2d at 563-64; Gordon, 438 F.2d at 877; see also Esser, 520 F.2d at 218 (“[s]ummary testimony does not allow witness to invade the province of the jury”).
The defendants also had full opportunity to cross-examine Kasper, further alleviating any danger of inaccuracy or unfair characterization. See United States v. King, 616 F.2d 1034, 1041 (8th Cir.), cert. denied, 446 *122U.S. 969, 100 S.Ct. 2950, 64 L.Ed.2d 829 (1980); Gordon, 438 F.2d at 876-77. They argue nonetheless that by restricting his summary to testimony given during direct (rather than cross) examination of government witnesses, Kasper undermined their ability to cross-examine him. However, they point to no instance where the cross-examination of a witness whose direct testimony was summarized would have changed the summary. Defendants cite Flemister v. United States, 260 F.2d 513 (5th Cir.1958), for the proposition that a summary witness must present “a full and even handed summary.” Reply Brief for Appellants at 52. But Flemister clearly declares: “A summary, to be admissible, we think need not give effect to the contentions of the accused.” Id. at 517. Flemister only required that the summary be what it purports to be. Id. Since Kasper never purported to do more than summarize the government’s evidence on cash flows, his testimony was in accord with Flemister. The defense specifically points to the trial judge’s refusal to allow cross-examination about Interconex’s cost of shipping as indicative of unfairly circumscribed cross-examination. Brief for Appellants at 54. But that question was outside the scope of the witness’s direct testimony, which dealt only with cash flows, and would have required the witness to refer to statements not in evidence. Tr. at 2053-54. The cross-examination at voir dire, where the defense repeatedly questioned the accuracy of the summary and convinced the trial judge to bar testimony based on one of the four summary charts the government hoped to introduce, further indicates that the cross-examination was not unfairly circumscribed. Tr. at 2002-03.
True, Kasper did not prepare the summary charts himself. Cf. Gordon, 438 F.2d at 877 (noting with approval that agent who prepared the chart was available for cross-examination). Kasper, however, had carefully reviewed the charts and ensured that they reflected information contained in documents already in evidence. He was able to identify the source of all the information on the chart and to explain how all the dollar figures were derived. The defense counsel also made the jury well aware that Kasper had not prepared the charts. Tr. at 2036-37. Although we believe the better practice is to require that summary charts be prepared by the witness, in this case the fact that Kasper did not prepare the charts in no way hampered the defendants’ ability to cross-examine him, and therefore did not prejudice the defense.
A second danger posed by summarized evidence is the subtle .introduction of otherwise inadmissible evidence. Rule 1006 was not meant to relieve the government of its obligation to lay a sufficient foundation for any evidence it expects the jury to consider. “Requiring the proponent [of a summary] to show the admissibility of the underlying materials is necessary to protect the integrity of the Federal Rules [of Evidence].” Johnson, 594 F.2d at 1255; see also United States v. Goss, 650 F.2d at 1344 n. 5; King, 616 F.2d at 1041. The defendants contend that some of Kasper’s testimony was inadmissible because he based it on material not in evidence. Although Kasper relied on out-of-court statements for his understanding of some of the financial transactions, he did not testify about anything other than what was already in evidence.33 Hence, the defendants’ contentions that Kasper introduced otherwise inadmissible evidence are unfounded.
A third danger posed by summaries of evidence is that they provide an extra summation for the government that comes from the witness stand rather than the counsel’s lectura. The distinction between valid summary testimony and argument is not a bright line. The task of organizing testimony can quickly turn into the marshalling of facts to support a particular position. But the word “argument” con*123notes a taking of sides in a controversy.34 Thus, a summary should not draw controversial inferences or pronounced judgment; these functions are best left to the closing argument of counsel. Here, however, the summary involved only routine computations and culling through of documents to eliminate confusing and extraneous evidence. Consequently we find no force to the argument that Kasper’s testimony provided an unwarranted second closing for the government.
We have reviewed in detail the summary of evidence provided by Kasper and we find that the summary did not stray from evidence already presented. The district court carefully considered the need for a summary after hearing all the government’s witnesses testify, and felt that the jury would benefit from the summary testimony. Thus, allowing Kasper to testify was no abuse of discretion by the district court.
B. Excluded Defense Exhibits
The defendants appeal the district court’s exclusion of three documents that they attempted to put into evidence. Two of the documents (DX201, DX203) were internal memoranda prepared as part of Raytheon’s own investigation of the Saudi Arabia housing contracts. The third excluded document (DX155) was a memorandum setting forth projected freight rates for shipping goods with Waterman, written before Raytheon entered into the Waterman shipping agreement. The defendants argue that these excluded exhibits are important corroboration of Lemire’s testimony that he pursued Raytheon’s best interests at all times during the bidding for the Saudi Arabia housing contracts.
1. Exhibits DX201 and DX203
The government objected to admission of both memoranda, DX201 and DX203, as hearsay, and the district court sustained its objection. The defendants’ claim that although the memoranda clearly are hearsay, they come within the “business records” exception to the hearsay rule. Federal Rule of Evidence 803(6), the codification of this exception, requires that a “memorandum of events ... [be] made at or near the time [of the events]” and that “it [be] the regular practice of that business activity to make the memorandum.” We agree with the district court that neither DX201 nor DX203 meets either criteria.
DX201 was prepared by Lemire for his superior on November 5,1976, and summarized why he had decided it was advantageous for Raytheon to award the housing contract C & F. By his own admission, it provides “a history and background of the transaction” from December 5,1975 to June 19, 1976, when the second housing contract was awarded to IMS. See Lodged Materials at 3. The lengthy interval between the time the memorandum was written, and some of the events it describes (one year and ten months) does not meet the exception’s “timeliness requirement,” and therefore it is not admissible under Rule 803(6). See United States v. Kim, 595 F.2d 755, 760 (D.C.Cir.1979) (timeliness requirement not waived even if accuracy of information not suspect). DX203, prepared by Mr. Wax-man, a subordinate of Lemire, was a review of the entire history of the two modular housing contracts with IMS, and was written after Lemire left the company. Since it was written after the Lemire memo and describes events that occurred during the same time period as those in the earlier memo, it too suffers from being untimely.
Additionally, both memoranda were not admissible under Rule 803(6) because it was not a regular business practice to make memoranda detailing the history of contracts Raytheon awarded. See Palmer v. Hoffman, 318 U.S. 109, 63 S.Ct. 477, 87 L.Ed. 645 (1943). “When a document is *124made for something other than a regular business purpose, it does not fall within the business records exception.” Kim, 595 F.2d at 761 (emphasis supplied). We think that memoranda prepared as part of an investigation into substantial abnormal procedures are not prepared for a regular business purpose. We find such memoranda similar to accident reports, which generally are not admissible as business records. See Palmer v. Hoffman, 318 U.S. at 113, 63 S.Ct. at 480.35 Thus, the district court did not err in excluding DX201 and DX203.
2. Exhibit DX155
DX155 (dealing with pre-contract proposed Waterman freight rates) was excluded on the grounds that it was irrelevant, because the company had entered the Waterman contract by the time Lemire let the housing contract. The government argues that the Waterman contract rate is the only pertinent rate for comparison to Interconex’s rate. The relevance of DX155 cannot so easily be dismissed, however, since it may have contained additional information about prevailing freight rates that would demonstrate Lemire acted reasonably in accepting the Interconex rate. Any error in excluding DX155 was harmless, however, because Lemire was allowed to testify about the substance of the memo. See Tr. at 2218. DX155 was thus cumulative, and it was within the trial judge’s discretion to exclude it. See Hamling v. United States, 418 U.S. 87, 127, 94 S.Ct. 2887, 2912, 41 L.Ed.2d 590 (1974) (“[t]he District Court retains considerable latitude even with admittedly relevant evidence in rejecting that which is cumulative”).
IV. Sufficiency of Evidence Against Achuck
Achuck challenges the government’s evidence against him as insufficient to support his conviction. He points out that “[t]here was no proof whatsoever that [he] played any role in the submission of the Interconex/IMS bid to Raytheon, or that he attended any meetings or had a single conversation concerning the modular housing shipping contract prior to Raytheon’s takeover of the fourth charter.” Brief for Appellants at 61-62.
In reviewing the evidence for sufficiency, we must consider all of the evidence in the light most favorable to the government. Glasser v. United States, 315 U.S. 60, 62 S.Ct. 457, 86 L.Ed. 680 (1942); United States v. Lewis, 626 F.2d 940, 951 (D.C.Cir. 1980); Crawford v. United States, 375 F.2d 332, 334 (D.C.Cir.1967). We must also accept “all reasonable inferences supporting the verdict.” United States v. Habel, 613 F.2d 1321 (5th Cir.), cert. denied, 447 U.S. 925, 100 S.Ct. 3018, 65 L.Ed.2d 1117 (1980); see also United States v. Skinner, 425 F.2d 552, 554 (D.C.Cir.1970). With this in mind, we find sufficient evidence to support Achuck’s conviction.
The evidence showed that Achuck was intimately involved in setting up various offshore accounts through which the defendants channelled the money Raytheon paid for shipping. These accounts were established just prior to the award of the IMS contract for housing. The evidence suggests that they served no function other than as a conduit for money paid as part of that contract. Thus, a jury might reasonably infer that Achuck set up those accounts because he had foreknowledge that Interconex would get the bid for shipping the housing to Saudi Arabia, and that that venture would generate excessive profits. In light of these financial dealings, it is significant as well that Achuck cannot otherwise explain the hidden receipt of $500,-000 from the shipping contract. The jury could have reasonably inferred from *125Achuck’s receipt of his share of the scheme’s bounty that he knew of the scheme.
Achuck seems to believe that because he did not participate in, or even know about, the actual mechanism by which the others perpetrated the fraud he cannot be convicted. This is not so.36 The evidence detailed above was certainly sufficient to support a finding that Achuck conspired to commit fraud on Raytheon. Thus, he can also be convicted of the substantive offenses of wire fraud and transporting securities taken by fraud based on the foreseeable acts of his co-conspirators perpetrated in furtherance of the conspiracy. Pinkerton v. United States, 328 U.S. 640, 66 S.Ct. 1180, 90 L.Ed. 1489 (1946). We thus uphold the jury’s conviction of Achuck.
V. Restitution
Stephens and Achuck37 attack the validity of the district court order conditioning their suspended sentences on respective restitution of $1,000,000 and $750,000 to Raytheon. They argue first that the district court may not order restitution because the jury verdict does not depend on a finding of an actual monetary loss to Raytheon. Second, even if the district court is authorized to order restitution as a condition of probation for the suspended sentences, Stephens contests his particular restitution amount as arbitrary and unsupported by any finding by the district court.
We start from the premise that the trial judge has wide discretion in sentencing including the setting of conditions on probation and the ordering of restitution. See United States v. Mitsubishi International Corp., 677 F.2d 785, 787 (9th Cir. 1982) (ordering contribution to National Alliance for Business program); United States v. Roberts, 619 F.2d 1, 2 (7th Cir. 1979) (ordering restitution). This assumption is supported by the language of the Probation Act, 18 U.S.C. § 3651 (1976), which authorizes restitution as a condition of probation. It provides:
*126Upon entering a judgment of conviction of any offense not punishable by death or life imprisonment, any court having jurisdiction to try offenses against the United States when satisfied that the ends of justice and the best interest of the public as well as the defendant will be served thereby, may suspend the imposition or execution of sentence and place the defendant on probation for such period and upon such terms and conditions as the court deems best.
So long, then, as restitution in any particular case is designed to further rehabilitation of the defendant without overly sacrificing society’s interests in deterrence, retribution and community safety, we should presumably uphold the order of the trial judge. See United States v. Restor, 679 F.2d 338, 340 (3d Cir.1982); United States v. Margala, 662 F.2d 622, 627 (9th Cir.1982) (as amended) (flexible standard required by “uncertainty about how rehabilitation is accomplished”) (quoting United States v. Consuelo-Gonzalez, 521 F.2d 259, 264 (9th Cir.1975)).
The defendants, however, premise their appeal against the condition of restitution on other, more specific, language later in the Probation Act:
While on probation and among other conditions thereof, the defendant—
May be required to make restitution or reparation to aggrieved parties for actual damages or loss caused by the offense for which conviction was had
18 U.S.C. § 3651 (1976). Courts construing the Act have interpreted this language as “limiting restitution to amounts for which the defendant is actually convicted.” United States v. Orr, 691 F.2d 431 (9th Cir.1982) (citing cases in accord); see also United States v. Johnson, 700 F.2d 699 (11th Cir. 1983); United States v. Brown, 699 F.2d 704 (5th Cir.1983); United States v. Follette, 32 F.Supp. 953 (E.D.Pa.1940) (first stating this construction). Relying on such holdings, the defendants read this language to preclude the trial judge from ordering restitution unless the jury verdict included a determination of loss to the victim in a determined amount. They claim that without this determination, a subsequent civil suit is the only means of evaluating the loss contemplated by § 3651. Brief for Appellants at 71-72, (quoting Best & Birzon, Conditions of Probation: An Analysis, 51 Geo. L.J. 809, 828 (1963)). The defendants’ position, which treats the requirements for proof of pecuniary loss due to criminal activity as equivalent to those for proof of loss due to civil wrongs, however, ignores the state’s important interests in rehabilitation and justice that are furthered by restitution.38 “Probation is part of the composite sanction imposed for law violation, and the validity of probation conditions is to be viewed in that light, not weighed in isolation.” United States v. Tonry, 605 F.2d 144 (5th Cir.1979). In addition, the defendants’ position is eroded by recent case law which generally holds that once the defendant has been convicted the trial judge may order restitution for the amount of loss she finds the criminal violation caused.39 See, e.g., Johnson, 700 F.2d 699; United States v. Lynch, 699 F.2d 839, 845-46 (7th Cir.1982); Brown, 699 F.2d at 711-12; Roberts, 619 F.2d at 2. But cf. United States v. Tiler, 602 F.2d 30, 34 (2d Cir.1979) (affirming order but noting that if district court had ordered restitution rather than a bond to ensure payment of loss to be determined in *127later proceeding, that would raise a “[d]ifferent question”).
We turn then to determine whether the district court abused its authority when it set restitution for Stephens and Achuck. The only limits on the court’s discretion to set restitution, aside from the defendants’ ability to pay, see Bearden v. Georgia,-U.S. -, 103 S.Ct. 2064, 76 L.Ed.2d 221 (1983), are that the restitution further the rehabilitation of the defendant, see Margala, 662 F.2d at 627, and that the restitution reflect Raytheon’s actual loss due to defendants’ illegal conduct. See Lynch, 699 F.2d at 845-46; Orr, 691 F.2d at 432-33. Of course, since it would constitute an abuse of discretion for the district court to assess restitution that exceeds the loss caused by the illegal activity, it would have been helpful for the district court to have made findings of fact elucidating the basis for its monetary assessment. Here the district court made no such findings. For this reason the defendant Stephens contends that the court acted arbitrarily in setting the amount of restitution. We do not so find.
We agree that where the trial record does not clearly support the district court’s assessment of loss due to illegal activity, the court must support its restitution order with additional findings of fact. Failure to so justify the amount of restitution would leave a reviewing court in the dark as to whether the amount was legal, and would require us to reverse and remand for factual findings. See, e.g., Johnson, 700 F.2d at 701-02 (remanding for district court to entertain such arguments as would be appropriate in support of a motion challenging a sentence as illegal); Brown, 699 F.2d at 712 (remanding for findings of fact because trial judge explicitly relied on presentence report in fashioning restitution, and that report was not in the record). Here, however, the record was sufficiently clear for us to competently determine that the district court’s restitution order was proper. The evidence indicated that Raytheon lost $600,000 to $900,000 on each of the first three shipments of housing by not chartering a boat itself. Tr. 971, 975. In addition, independent evidence showed that $2,131,-480 from the Interconex shipping contract went to GH, and was subsequently split, probably evenly, between Lemire, Carver, Stephens and Achuck. Thus, the district court could have properly assessed $1 million restitution against Achuck and Stephens as “the principals of Interconex.” Sentencing of Stephens at 35.40 The court chose to order Achuck to pay only $750,000 to Raytheon, presumably reflecting its assessment that Achuck was less culpable and demonstrated a more penitent attitude. See Sentencing of Achuck at 19-20. Thus, despite the lack of a rationale for the amount of restitution articulated by the district court, the record supports its order as within its discretion.
Conclusion
Despite the fact that the government advanced on appeal an interpretation of wire fraud that goes beyond the bounds of what we believe the statute prescribes, we do not discern any prejudicial error prompted by that interpretation in this case. In light of the instructions, the arguments and the *128jury verdicts themselves, we are confident that the jury convicted the defendants only after finding that the defendants’ scheme contemplated a pecuniary loss of some kind to Raytheon. In addition, we fail to perceive any prejudice to the defendants caused by other alleged errors cited on appeal. We therefore affirm the convictions.
. A freight forwarder is a commissioned agent that books shipments with common carriers for ocean freight transportation. It may also charter space on a vessel or charter an entire vessel for a particular customer,
.The shipping rates in the other bids were $115.07 per ton by Bendix, and $125.39 per ton by Atlantic International. Westyield Company also included a bid based on the $20.50 per cubic foot price quoted it by Interconex, but it bid on only part of the contract, and apparently its houses were too small for Raytheon’s needs.
. Interconex maintained that Raytheon had no right to know its costs since the contract was for a fixed rate. Interconex also persuaded IMS not to reveal the information for the same reason.
. The case against Carver was severed from this case on the government’s motion, and Carver later pleaded guilty.
. The government argued at trial that Lemire provided information about the contract specifications to IMS during the June 9th conversation. The defense contended that the discussion focused generally on housing for Saudi Arabia, but did not reveal any contract specifications.
. The requisite elements of “scheme to defraud” under the wire fraud statute, 18 U.S.C. *108§ 1343 and the mail fraud statute, 18 U.S.C. § 1341, are identical. Thus, cases construing mail fraud apply to the wire fraud statute as well. See United States v. Feldman, 711 F.2d 758, 763 n. 1 (7th Cir. 1983); United States v. Computer Sciences Corp., 689 F.2d 1181, 1188 n. 14 (4th Cir.1982), cert. denied, 459 U.S. 1105, 103 S.Ct. 729, 74 L.Ed.2d 953 (1983); United States v. Giovengo, 637 F.2d 941, 944 (3d Cir. 1980), cert. denied, 450 U.S. 1032, 101 S.Ct. 1743, 68 L.Ed.2d 228 (1981).
.18 U.S.C. § 1343 provides:
Whoever, having devised or intended to devise any scheme or artifice to defraud, or for obtaining money or property by means of false or fraudulent pretenses, representations, or promises, transmits or causes to be transmitted by means of wire, radio, or television communication in interstate or foreign commerce, any writings, signs, signals, pictures or sounds for the purpose of executing such scheme or artifice, shall be fined not more than $1,000 or imprisoned not more than five years or both.
. In Reid, we quoted with approval the Fifth Circuit’s comment that “[t]he law does not define fraud; it needs no definition; it is as old as falsehood and as versable [sic] as human ingenuity.” Weiss v. United States, 122 F.2d 675, 681 (5th Cir. 1941). The government’s expansive interpretation in this and other recent mail and wire fraud cases, see, e.g., United States v. Feldman, 711 F.2d at 764; Von Barta, 635 F.2d at 1003, gives us second thoughts.
. The phrase was first used in the mail fraud statute of 1872. Ch. 335, § 301, 17 Stat. 323. See Comment, The Intangible-Rights Doctrine and Political Corruption Prosecutions Under the Federal Mail Fraud Statute, 47 U.Chi.L.Rev. 562, 567 (1980).
. See, e.g., Coffee, The Metastasis of Mail Fraud: The Continuing Story of the “Evolution” of a White Collar Crime, 21 Am.Crim.L. Rev. 1 (1983); Coffee, From Tort to Crime: Some Refíections on the Criminalization of Fiduciary Breaches and the Problematic Line Between Law and Ethics, 19 Am.Crim.L.Rev. 117 (1983) [hereinafter cited as Coffee, From Tort to Crime]; Hurson, Limiting the Federal Mail Fraud Statute — A Legislative Approach, 20 Am.Crim.L.Rev. 423 (1983); Comment, supra note 9.
In corporate law, the notion of what constitutes fraud on a company by a senior official as opposed to a mere conflict of interest, which may be approved in advance or even ratified in retrospect by the company’s governing board, has changed considerably over the past several decades. See 3 Fletcher Cyclopedia Corporations § 917, at 371 (perm. ed. 1975). This is reflected in recent state laws, see, e.g., Del. Code Ann. tit. 8, § 144(a) (1969) (no contract void or voidable if fair or if material facts of transaction revealed at time it is ratified); N.Y. Bus.Corp. Law § 713 (McKinney Supp.1982) (same), and the Model Business Corporation Act § 41 (1979). In general, where an official of the corporation does not disclose his personal interest in a transaction the transaction is merely voidable and the company may choose to go ahead with the transaction as well as continue with the official’s services, see 3 Fletcher Cyclopedia Corporations, supra, §§ 979, 981, at 496, 500, as long as the transaction is fair to the corporation. Id. § 919, at 377, 378. This reading of corporate law parallels the civil law’s treatment of non-disclosure generally: non-disclosure is material only if it was reasonably likely to affect a party’s judgment in a particular transaction. See Restatement (Second) Torts § 551(1); Restatement (Second) Contracts §§ 161, 162.
. “[I]f merely depriving the victim of the loyalty and faithful service of his fiduciary constitutes criminal fraud, the ends/means distinction is lost. Once the ends/means distinction is abolished and disloyalty alone becomes the crime, little remains before every civil wrong is potentially indictable.” Coffee, From Tort to Crime, supra note 10, at 167. Other types of intangibles featured in wire fraud cases are not mere means to pecuniary ends. Thus, a *110scheme to deprive someone of privacy, see Louderman, 576 F.2d at 1387-88, or to gain sexual favors, see Condolon, 600 F.2d at 8, can sustain a finding of criminal intent because they involve, intangibles recognized in law as having independent value to their owners. And, some intangibles like trade secrets, although a means to pecuniary ends, are so closely related to those ends that a scheme to deprive a victim of the intangible necessarily implies that the perpetrator contemplated pecuniary harm.
. “The requisite intent under the federal mail and wire fraud statutes may be- inferred from the totality of circumstances and need not be proven by direct evidence.” United States v. Alston, 609 F.2d 531, 538 (D.C.Cir.1979), cert. denied, 445 U.S. 918, 100 S.Ct. 1281, 63 L.Ed.2d 603 (1980).
. Our holding does not address whether an undisclosed conflict of interest, by itself, can support the wire fraud conviction of a public official. Public officials may be held to a higher standard of public trust; and conflicts of interest may harm the public merely by giving the illusion of unfairness. See Ballard, 663 F.2d at 541 n. 17; United States v. Dixon, 536 F.2d 1388, 1400 (2d Cir.1976); see also United States v. Mandel, 591 F.2d 1347 (4th Cir.) (affirming conviction on theory independent of evidence of bribe), rev’d on other grounds, 602 F.2d 653 (4th Cir. 1979) (en banc), cert. denied, 445 U.S. 961, 100 S.Ct. 1647, 64 L.Ed.2d 236 (1980).
.See Ballard, 663 F.2d at 541; cf. United States v. Bronston, 658 F.2d 920 (2d Cir.1981) (upholding mail fraud conviction of a law firm partner who performed legal work for a company to help it obtain a city contract at the same time his firm was working to get the contract for a competitor), cert. denied, 456 U.S. 915, 102 S.Ct. 1769, 72 L.Ed.2d 174 (1982); United States v. Newman, 664 F.2d 12 (2d Cir.1981) (reversal of a dismissal of a mail fraud indictment of investment banking firms’ employees for insider trading on their own behalf based on confidential knowledge of impending corporate takeovers). While it is not at all clear, given the facts in these cases, that their results are inconsistent with our ruling, to the extent that their language or rationale cannot be squared with the holding in this case, we disagree with their analyses.
. The Ballard court rejected the argument that “the concealment by [an intermediary’s employee] was material ... because [the intermediary] might have desired to sell directly to FPC ... to gain favor with that customer for the future.” 663 F.2d at 541. By rejecting this argument, the court effectively asserted that general threats to business interests posed by employee conflicts of interest are too speculative to support a mail fraud conviction. The court demanded more specific evidence to back the government’s conjecture that the employee conflict hurt the intermediary. Id.
. The standard for determining when an-error in a jury instruction requires reversal is the general standard for determining harmless error after objection by the defense. See Hamling v. United States, 418 U.S. 87, 108, 94 S.Ct. 2887, 2902, 41 L.Ed.2d 590 (1973); Alexander, 418 F.2d at 1207; United States v. Valie-Valdez, 554 F.2d 911, 916 (9th Cir.1977). Under that standard, “[i]t is our responsibility ... to reverse appellant’s conviction unless we can say ‘with fair assurance after pondering all that happened without stripping the erroneous actions from the whole, that the judgment was not substantially swayed by the error.’ ” Alexander, 418 F.2d at 1207 (quoting Katteakos v. United States, 328 U.S. 750, 765, 66 S.Ct. 1239, 1248, 90 L.Ed. 1557 (1946)). Although jury instructions addressing the elements of a crime are crucial, and errors in them have great potential for unfairness, we do not find that the possibly confusing nature of a small portion of the instructions in this case infected the trial with an unfairness that violates the defendants’ rights to due process. Hence we do not consider whether the error was “harmless beyond reasonable doubt.” Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967) (constitutional error requires reversal unless “harmless beyond a reasonable doubt”).
. For example, in Pollack, a mail fraud case, the instructions stated that if the “appellants were ‘promoters of stock’ ... then [they] stood in a fiduciary relation to stockholders which required appellants to disclose fully all known facts that might influence prospective stockholders.” 534 F.2d at 972-73. The appellants challenged the instruction both as permitting conviction solely for breach of fiduciary duty and because the prosecutor had not introduced any evidence that the defendants were promoters. We affirmed the conviction, however, because “throughout his charge to the jury, Judge Gasch reiterated that actual fraud, defined in terms of specific intent and willfulness, was necessary to support a conviction.” Id. at 973.
. The full charge relating to the meaning of “scheme or artifice to defraud” read:
Now, the essential elements of the offense of wire fraud, each of which the government must prove beyond a reasonable doubt, are as follows:
The first essential element: The government must prove that one or more of the defendants devised or intended to devise a scheme or artifice to defraud, specifically, a scheme or artifice with one or both of the two following objectives:
Number one, the first alleged object was to defraud the Raytheon Company of its right to honest, conscientious, faithful, loyal, disinterested and unbiased services, actions, and performances of duties by its employees Carver and Lemire, free from bribery, corruption, partiality, willful omission, bias, dishonesty, deceit, misconduct and fraud.
And the second object or the second alleged object of the scheme or artifice was to obtain money from the Raytheon Company by means of false pretenses and representations which defendants knew would be and were false when made.
Now the words “scheme and artifice” as used in the wire fraud statute include any plan or course of action intended to deceive others and to obtain by false or fraudulent pretenses, representations or promises, money or property from persons so deceived.
Although the government need not show that the alleged victims were in fact defrauded, the government must prove beyond a reasonable doubt that some actual harm or injury was at least contemplated.
Now the object of the scheme need not be money or any form of tangible property. The government need not prove any actual loss of money by the Raytheon Company.
A scheme to defraud an employer of the honest, faithful and unbiased services of its employees can also come within the meaning of scheme or artifice to defraud as set forth in the wire fraud statute. Breach of an employee’s duty of loyalty to his employer does not, without more, violate the wire fraud statute. But such a breach by the employee can violate the wire fraud statute when, with specific intent to defraud, the employee also violates the employee’s duty to disclose material information to his employer, or makes a material misrepresentation to or actively conceals material facts from the employer.
Tr. at 3174-77.
.Generally the court must explain all terms of legal significance. United States v. Anderton, 629 F.2d 1044, 1049 & n. 5 (5th Cir.1980) (“agent” not self-defining). See, e.g., Perry v. United States, 422 F.2d 697 (D.C.Cir.1969) (instruction regarding use of “excessive force” in self-defense reversible error where it did not illumine boundary between reasonable and unreasonable force).
. At oral argument it became evident that the government, the defendants, and the panel all had different interpretations of Ballard’s materiality requirement.
. The district court’s exact prefatory remarks were:
Now, ladies and gentlemen, during the course of my discussions and instructions really — I guess I should say instructions with you concerning the various elements of the offenses charged in this indictment, I mentioned intent many times. In the wire fraud — in the wire fraud counts, counts one, three, four and five, and in the conspiracy count, count seven, I made it clear to you that one of the essential elements of each offense was specific intent.
Tr. at 3208.
.We reached a similar conclusion in Post, 407 F.2d at 329, where we found that the phrases “intentionally converted” and “knowingly use[d]” in the charge sufficiently apprised the jury of the need to find specific intent to defraud. In Post, the district court had stated in a prior instruction that the jury was to acquit if it found that a golf club’s directors used the club’s funds for the club’s benefit. Id. at 328; see also Feldman, 711 F.2d at 765 (“intent to defraud” not in statement of elements of mail . fraud, but definition elsewhere made clear that jury could only convict if it found that defendant committed acts with purpose of defrauding employer).
. We find it significant that in his closing argument summing up the government’s proof, the prosecutor explicitly and exclusively spoke of receipt of a $2.1 million dollar kickback:
The government has proved essentially that four men and a corporation took $2 million, one hundred-and-some odd thousand from the Raytheon Company by fraud in an agreement in which they agreed with two employees of the Raytheon Company to give them a payoff, a kickback, a bribe — whatever you want to call it — of over a million dollars in order that they be given the contracts which generated those two million dollars. That’s what it all really boils down to.
Tr. at 2904. Conversely, we find unpersuasive defendants’ suggestion that the government’s closing argument “played upon the theme” of mere failure to disclose Lemire’s and Carver’s conflict of interest. Brief for Appellants at 31. The prosecutor himself focused on the need to show the defendants’ specific intent to defraud Raytheon of money when he argued:
I would like to say also that while I will make these remarks, remember that the United States has proved that each of the defendants received approximately a half-a-million dollars of the proceeds in this case. I make that point to you so that as I go through the evidence, you can use that fact to consider what did they feel, what did they think, what did they intend, when they did a particular act. It is very important to consider that when going through the evidence, and I would like for you to remember that fact.
An act may be totally meaningless; it may be innocent, but when considering the fact that — for example, when Mr. Lemire awarded contracts to IMS, it is important to consider that the evidence has shown that at least $400,000, which came directly out of
that contract, went into the bank account of his in the Caymun Islands. You have to review and look at why did he let that contract.
• You have to consider what must have been in his mind when he did that act or some other act that I will be touching upon. It is somewhat like reviewing a movie when you know what the ending is. Sometimes when you are looking at a movie you say to yourself, “I wonder why he did this?” or, “I wonder why that happened?” If you know the ending and you look at the movie again, you know exactly the why’s and wherefore’s.
It is also important because the Government has to prove to you that each of these defendants specifically intended to defraud the Raytheon Company, and we can’t prove to you by some picture in the defendants’ mind what was going on in his mind when he did something, and it is important to remember that — the totality of what we have shown.
Tr. at 2911-12. In fact, the prosecutor’s argument consistently played on the theme that in addition to the undisclosed conflict of interest, defendant Lemire’s activity indicated that he did intend to deprive Raytheon of money or shipping opportunities. See, e.g., Tr. at 2921 (“If [Lemire] had been truly faithful to his duties and responsibilities to his employer he would have looked into [IMS contentions that the shipping costs were high] ... [B]ut he didn’t ... because he didn’t want anybody taking a hard, long look at that transportation because he knew he was getting a piece of it.”); Tr. at 3103-04 (“The mere fact that Mr. Lemire let these contracts C & F is not criminal .... The point here is if [sic] Mr. Lemire made the choice to go C & F because he firmly believed that it saved money, or did he go C & F because he was being paid a half million dollars.”).
. The defendants clearly acquiesced at that time in the part of the charge with which we have the most trouble — that “[a] scheme to defraud an employer of the honest, faithful, and unbiased services of its employees can also come within the scheme to defraud.” See Tr. at 2877 (statement of defense counselor Vardaman) (“it is not necessary to go on for a full page” since “one of the objects your honor is going to instruct will be if Raytheon is defrauded of the honest and faithful services of Mr. Carver and Mr. Lemire”).
. Where, as here, the defense fails to specify sufficiently the portion of the charge to which it objects, and therefore fails to comport with Rule 30, we will reverse only if the instruction is “plain error” — if the error causes a substantial miscarriage of justice. See, e.g., United States v. Baker, 693 F.2d 183 (D.C.Cir.1982) (no miscarriage of justice since evidence against defendants is overwhelming); Campbell, 684 F.2d at 149 (although instructions technically could have allowed jury to convict for bribery based on what is merely receipt of illegal gratuities, fact that evidence focused on activity that would constitute bribery meant that “[i]n the context of the trial as a whole, [instructions were] not plain error”). Since in this case we find the confusing instructions were not prejudicial, they certainly do not constitute plain error.
Of course, for those objections that the defendants raised with sufficient particularity to apprise the trial judge of their dissatisfaction, we do not demand “plain error” in order to reverse. The only relevant specific objection that the district court did not accommodate was the defendants’ suggestion that the court instruct on the distinction between active and constructive fraud. See Tr. 2878. But the inclusion of the words materiality and specific intent, for which the defense asked, along with its own proposed definition of intent to defraud clearly covered the same territory. Thus, the district court’s failure to explicitly state that mail fraud must be “active” was, at worst, harmless error.
. Variance between instructions and the indictment can also raise a charge that the defendant is “unprotected against prosecution for the same offense.” United States v. Freeman, 514 F.2d 1184, 1189 (10th Cir.1975); see also Berger, 295 U.S. at 82, 55 S.Ct. at 630. The variance of the instructions from the indictment in this case, however, presents no possibility of double jeopardy, since both clearly charge the same offense based on the same conduct so that further prosecution for that offense would be barred. See Mangieri, 694 F.2d at 1278 n. 7; Freeman, 514 F.2d at 1189.
. We reach' this conclusion only after our determination that it was highly improbable that the jury would have interpreted the instructions to convict solely for failure to disclose a conflict of interest which held no potential for specific business harm to Raytheon.
. The exact language of this part of the indictment charges that:
defendants Roy R. Carver, Joseph C. Lemire, Lionel W. Achuck, Jon T. Stephens, and Interconex, Inc., together with others known and unknown to the Grand Jury, devised and intended to devise and employ a scheme and artifice (1) to defraud the Raytheon Company of its right to the honest, conscientious, faithful, loyal, disinterested and unbiased services, actions and performance of duties by its employee, Roy R. Carver and Joseph C. Le-mire, free from bribery, corruption, partiality, wilful omission, bias, dishonesty, deceit, misconduct and fraud and (2) to obtain money from the Raytheon Company by means of false pretenses, and representations, which defendants well knew would be and were false when made.
J.A. at 137.
.Considerable deference should be given to the views of the trial judge on matters of surprise. The trial judge listened to all the testimony and the opening statements, before the defense counsel objected to the modified instruction at the pre-charge conference. The judge stated that she did not understand either the case or the original charge as having been based on a theory that required the government to prove both objects of the scheme. See Tr. at 2875.
. Fed.R.Evid. 602 provides:
A witness may not testify to a matter unless evidence is introduced sufficient to support a finding that he has personal knowledge of the matter .... This rule is subject to the provisions of rule 703, relating to opinion testimony by expert witnesses.
. Fed.R.Evid. 1006 provides:
The contents of voluminous writings, recordings or photographs which cannot conveniently be examined in court may be presented in the form of a chart, summary, or calculation. The originals, or duplicates, shall be made available for examination or copying, or both, by other parties at reasonable time and place. The court may order that they be produced in court.
. Before Kasper testified, Judge Johnson told the jury:
[T]he testimony of an accountant — and that is what Mr. Kasper is — and the prepared charts and summaries that he will show you, have been received for the sole purpose of explaining facts disclosed by books, records, other documents, and testimony; in other words, evidence in this case.
Such charts and summaries, as you see there, are not, in and of themselves proof of any facts. If such charts and summaries do not correctly reflect the facts or figures shown by the evidence, as you have heard in this case, then you should totally disregard those charts.
In other words, such charts or summaries are used only as a matter of convenience.
So if, and to the extent that, you find that they are not in truth summaries of facts or evidence of figures shown by evidence, as you have heard it, you are to disregard them entirely.
Tr. at 2021-22.
. Since the judge, prosecutor and defense counsel all heard the evidence upon which Kasper based his summary, he was unlikely to stray from that evidentiary base without quickly being stopped. In fact, at one point the witness inadvertently started to discuss material not in evidence, and the prosecutor prevented him from doing so. See Tr. at 2024, 2404.
. “Argument” means:
a coherent series of reasons, statements, or facts intended to support or establish a point of view: a discussion often involving a controversial topic.
Webster’s Third New Int’l Dictionary 116 (1976).
. The defendants urge that “modem courts have severely limited [Palmer’s] application under the [Federal] Rules [of Evidence]. ’ ’ Reply Brief for Appellants at 27. They cite Gardner v. Chevron U.S.A. Inc., 675 F.2d 658, 660 (5th Cir.1982) in support of this proposition. But Gardner held that the trial court’s admission of an accident report was error. It did consider that error harmless but only because a hearing determined that no one either showed or read the accident report to the jury. Gardner clearly demonstrates that the district court correctly excluded DX201 and DX203.
. Although the evidence against Achuck does not indicate that he knew the precise mechanism by which the fraud was perpetrated, it is similar in nature to that found sufficient to convict the defendant in United States v. Tilton, 610 F.2d 302 (5th Cir.1980). Tilton was responsible for contracting out some of his employer’s work. He received a kickback from the shops to which he provided the work, and, to pay this kickback the shops padded the invoices to Tilton’s employer. There was no evidence that Tilton knew of the padded invoices by which the scheme to defraud was consummated. Nonetheless, the court upheld the jury verdict finding him guilty of mail fraud because it found the inflated invoices were a natural consequence of the unlawful agreement or kickback. Tilton should have known that the money had to come from somewhere and, the most likely source would be Tilton’s employer since the bribe was in exchange for that contract. Id. at 308. Similarly, Achuck had reason to foresee that the money paid to GH, and ultimately to Lemire, Carver, Achuck, and Stephens, which had to come from somewhere, would most likely have come as a result of the IMS contract in which Interconex participated.
. The government argues that Achuck waived his right to challenge the restitution order on appeal because Achuck’s sentencing memorandum filed the day before sentencing, stated:
Consistent with Mr. Achuck’s sincere feeling of sorrow and remorse, he is fully prepared to make restitution in any amount the court considers appropriate without any challenge whatsoever.
Achuck now argues that this waives only his right to challenge the amount of restitution, not his right to challenge the imposition of restitution in the first place. He points out that at the time the memorandum was written the district court had already stated that it would impose restitution. The fact remains, however, that Achuck never communicated the nature of his problem with restitution to the sentencing judge, and preservation of the point on appeal requires communication of some sort of comprehensible challenge to the sentencing court. See, e.g., State v. Garner, 115 Ariz. 579, 566 P.2d 1055 (Ct.App.1977) (defendant’s failure to object to amount of restitution order and the procedure by which it was set bars due process challenge on appeal). We need not reach the question of whether Achuck could have waived a challenge to the amount of restitution ordered when that amount was not yet determined, since we find below that the amount was supported by the record. Biddy v. State, 138 Ga. App. 4, 8, 225 S.E.2d 448, 451 (1976) (amount of restitution sustained only because it was not contested at sentencing); Commonwealth v. Walton, 483 Pa. 588, 397 A.2d 1179 (1979) (same).
. Consistent with this position, one court upheld an order that a defendant pay restitution in a criminal case although he had been absolved of all civil liability in a civil suit concerning the illegal conduct. See Gross v. United States, 228 F.2d 612 (8th Cir.1956). The defendant was incorporator, president, and a stockholder in a company found civilly liable, but Iowa law precluded personal liability against the defendant. Id. at 615.
. Some of the cases the defendant cites as limiting restitution merely stand for the proposition that courts cannot order defendants to pay for losses due to criminal conduct charged in counts to which they neither pled guilty nor were found guilty. See, e.g., United States v. Orr, 691 F.2d at 433-34.
. The district court recognized that the money was probably split four ways. It decided, however, to assess restitution only against Stephens and Achuck, stating:
I can and shall require restitution from the principals of Interconex, because you, in my view, the principals of Interconex, defrauded Raytheon.
Now you may have chosen to give some money to Mr. Lemire or you may have chosen to give some money to Mr. Carver. I don’t know. But I do know you defrauded Raytheon and you could do whatever you wanted with that money that you defrauded
them of, but I’m going to see to it that you give Raytheon its money back.
Now you can file suit against Mr. Lemire, and if you believe you gave money to Mr. Carver, you can file suits against him too, but the principals of Interconex are indeed going to pay this money back to Raytheon.
Sentencing of Stephens at 35. Given the court’s judgment, based on the evidence as to who initially received the benefits of the scheme, that the principals of Interconex were the real masterminds of the scheme, ordering Achuck and Stephens to repay virtually all losses was not an abuse of discretion.