UNITED STATES OF AMERICA, PLAINTIFF-APPELLEE,

v.

HARRY V. MOHNEY, DEFENDANT-APPELLANT

RYAN, Circuit Judge.

Defendant Harry Mohney appeals his conviction for filing false individual income tax returns, in violation of²⁶ U.S.C. § 7206(1), and aiding and assisting in filing false corporate tax returns, in violation of²⁶ U.S.C. § 7206(2). The following issues are before us on appeal:

1. Whether prosecutorial misconduct and judicial errors deprived Mohney of a fair trial and the right to present a defense;

2. Whether the district court erred in denying the motion to suppress evidence obtained through a search warrant;

3. Whether the district court abused its discretion in rulings regarding the summary witness testimony;

4. Whether the district court erred in denying the motion for judgment of acquittal based on the insufficiency of the evidence;

5. Whether the district court erred in refusing Mohney’s motion to dismiss Counts IV-YI based on a closing agreement Mohney reached with the IRS; and

6. Whether the district court impermis-sibly restricted Mohney’s right to present a defense by refusing to permit him to examine witnesses concerning the closing agreement and by quashing subpoenas of witnesses to testify regarding the agreement?

We agree with the district court’s disposition of these matters and therefore affirm.

I.

In 1966, Harry Mohney began acquiring what are euphemistically known by some as “adult entertainment” businesses which he ran as a sole proprietorship. These businesses included theaters, bookstores, peep machines, and novelty and film distributors, all featuring sex-oriented “entertainment.” He organized each aspect of the business as a separate corporation. Most of these businesses had offices in Durand, Michigan. Mohney formed Modern Bookkeeping Services (“MBS”) to handle and centralize the bookkeeping and tax preparation aspects of his businesses. He hired Elizabeth Scribner as the manager of MBS.

In 1984, federal agents, investigating a pattern of arsons at adult theaters, executed a search warrant of MBS headquarters. During the search, agents seized $400,000 in currency and records indicating that Mohney had not declared income collected from International Amusement’s (“IA”) peep machines. The income was skimmed by the route drivers who, after collecting coins from the peep machines, paid the location managers a “split” prior to recording the coins as income in the corporation’s books. Based on these records, the government obtained an indictment against Mohney and three MBS employees.

Count I charged Mohney, Scribner, Thomas Tompkins (MBS’ accountant), and Lee Klein (an attorney retained by MBS) with conspiring to defraud the IRS, in violation of 18 U.S.C. § 371. The district court dismissed this charge prior to trial. 723 F.Supp. 1197.1 The remaining counts named only Mohney. Counts II-IV charged Mohney with filing false individual income tax returns for the calendar years 1981-83, respectively, in violation of²⁶ U.S.C. § 7206(1). Counts V-YII charged that Mohney willfully aided and assisted in the filing of false corporate tax returns for Otis Mohney, Inc. (“OMI”), later IA, for the fiscal years 1982-84, respectively, in violation of²⁶ U.S.C. § 7206(2).

At trial, the government called fifty-two witnesses over a nine-week period. Many of these witnesses were former MBS employees who testified, under a grant of immunity, that Mohney was not actively involved in preparing the tax returns. Route drivers, who paid the splits to the location managers, also testified under immunity.

Key witnesses for the government were Kenneth and Barbara Goodrich, both of whom were directly involved with keeping IA’s books. Pursuant to an immunity grant, the Goodriches testified concerning a two percent bonus Kenneth received, based on the revenue of certain peep machines. The calculation of this bonus showed that the peep machines produced income that Mohney had not declared.

A number of witnesses, including both Mohney’s ex-wife and his former girlfriend, Gail Parmentier, testified that Mohney used cash to pay for living expenses, travel, family support, and film production. Witnesses involved in the sex-oriented film business testified that it was standard procedure to pay expenses for such films in cash. Parmentier also testified about her illicit relationship with Mohney.

The government concluded its case by presenting two summary witnesses, IRS Revenue Agents Robert Bednarczyk and Kenneth Peterson. Bednarczyk summarized the evidence regarding the corporate tax returns and presented his estimate of IA’s revenue understatement on the individual returns. Peterson summarized the evidence regarding the individual returns and gave an estimate of the understatement. The district court denied a defense motion to sequester these witnesses to prevent Peterson from relying on Bednarc-zyk’s testimony.

The government did not call MBS manager Scribner as a witness, although she had been listed on its witness list. The government also refused to grant her immunity. Mohney attempted to call her as a witness, but she filed an affidavit asserting that she would invoke her Fifth Amendment privilege if called. The government also did not call or grant immunity to accountant Tompkins or attorney Klein.

Mohney’s defense focused on his claimed peripheral and infrequent involvement with the businesses. He alleges that he was prevented from effectively presenting his defense because Jack Mohney, who handled IA’s revenues and splits, was deceased, and because the government refused to call the only witnesses with direct knowledge of the IA returns: Tompkins, Scribner, and Klein.

The jury found Mohney guilty on each charge. The district court sentenced him to concurrent three-year terms of imprisonment on Counts II-VI, imposed a four-year probation term on Count VII, and fined him a total of $255,000. The court also imposed a special condition of probation requiring Mohney to pay back taxes found to be due and owing by the IRS.

II.

A.

Right to a Fair Trial

Mohney contends that prosecutorial misconduct, compounded by the district court’s errors, denied him a fair trial. In evaluating this claim, we recall that “the touchstone of due process analysis in cases of alleged prosecutorial misconduct is the fairness of the trial, not the culpability of the prosecutor.” Smith v. Phillips, 455 U.S. 209, 219, 102 S.Ct. 940, 947, 71 L.Ed.2d 78 (1982).

1.

Immunity

Mohney alleges that the prosecutor’s refusal to grant immunity to Tompkins, Scribner, and Klein, who best understood MBS’ operations and were crucial to his defense, while granting immunity to 20 other witnesses, and after indicating that the three would receive immunity and testify, amounted to prosecutorial misconduct. Mohney also protests the district court’s refusal to compel the prosecution to grant immunity. The government responds that it is not obligated to grant immunity to key defense witnesses and that it properly refused to grant immunity to witnesses who were putative defendants.

The grant of immunity by a prosecutor is governed by 18 U.S.C. § 6002 et seq. This statute gives the executive branch sole authority to grant “use immunity” to witnesses. 18 U.S.C. § 6003; see also United States v. Hooks, 848 F. 2d 785, 798 (7th Cir.1988). In exercising this power, the statute gives the prosecutor considerable discretion to request immunity when “in his judgment” it is “necessary to the public interest.” Id. The statute does not require the government to grant a defense witness immunity. Id. at 799.

Two theories have emerged under which defendants would be entitled to a grant of immunity for prospective defense witnesses. The first theory, rejected by most courts, allows immunity for defense witnesses when necessary for an effective defense. The second theory provides immunity to remedy prosecutorial misconduct.

Under the effective defense theory, immunity is available when it is properly sought in the district court, the witness is available to testify, the proffered testimony is both essential and clearly exculpatory, and no strong governmental interests countervail against an immunity grant. Virgin Islands v. Smith, 615 F. 2d 964, 972 (3d Cir.1980). Although our circuit recognized the serious problems refusal to extend immunity may present for defendants wishing to introduce essential evidence not otherwise available, we have held that federal courts do not have the inherent power to immunize witnesses whose testimony is essential to an effective defense. United States v. Pennell, 737 F. 2d 521, 526-27 (6th Cir.1984), cert. denied, 469 U.S. 1158, 105 S.Ct. 906, 83 L.Ed.2d 921 (1985). We rejected this theory because it would violate separation of powers to recognize an inherent judicial right to grant immunity when immunity is a legislative creation explicitly entrusted to the executive branch. Id. at 527. Compelled judicial use immunity could also impair the subsequent prosecution of the witness. United States v. Thevis, 665 F. 2d 616, 640 (5th Cir.), cert. denied, 459 U.S. 825, 103 S.Ct. 57, 74 L.Ed.2d 61 (1982). If the government will be limited to prosecuting either the defendant or the immunized witness because it will not be able to prove that the immunized testimony would not taint the prosecution of the witness, the choice of which one to prosecute should rest with the government, not with the courts. Id.; Pennell, 737 F. 2d at 528. The majority of other circuits have also rejected this theory. United States v. Angiulo, 897 F. 2d 1169 (1st Cir.), cert. denied, — U.S. -, 111 S.Ct. 130, 112 L.Ed.2d 98 (1990); United States v. Paris, 827 F. 2d 395 (9th Cir.1987); United States v. Tindle, 808 F. 2d 319, 325 (4th Cir.1986), cert. denied, 490 U.S. 1114, 109 S.Ct. 3176, 104 L.Ed.2d 1038 (1989); United States v. Sawyer, 799 F. 2d 1494, 1506 (11th Cir.1986), cert. denied sub nom., Leavitt v. United States, 479 U.S. 1069, 107 S.Ct. 961, 93 L.Ed.2d 1009 (1987); Thevis, 665 F. 2d 616; United States v. Turkish, 623 F. 2d 769 (2d Cir.1980), cert. denied, 449 U.S. 1077, 101 S.Ct. 856, 66 L.Ed.2d 800 (1981); In re Daley, 549 F. 2d 469, 479 (7th Cir.), cert. denied, 434 U.S. 829, 98 S.Ct. 110, 54 L.Ed.2d 89 (1977); United States v. Graham, 548 F. 2d 1302, 1315 (8th Cir.1977); Earl v. United States, 361 F. 2d 531, 534-35 (D.C.Cir.1966), cert. denied, 388 U.S. 921, 87 S.Ct. 2121, 18 L.Ed.2d 1370 (1967).

Even if we accepted the effective defense theory, Mohney still could not prevail on the facts of this case. Immunity under this theory is not available if a strong countervailing government interest exists, such as a legitimate interest in prosecuting the witness where no appropriate safeguards are available. Smith, 615 F. 2d at 973. The government here indicted Tompkins, Scribner, and Klein, along with Mohney. Although the district court dismissed the charge in the indictment naming the three potential witnesses, the dismissal was subject to a motion to reconsider throughout trial and was reversed on appeal. Moreover, even if the appeal had failed, the prosecution could have pursued charges against Tompkins, Scribner, and Klein for conspiracy to file false returns. Thus, the prosecution had a legitimate interest in prosecuting the witnesses.

This circuit has yet to rule on the second theory for granting immunity, to remedy prosecutorial misconduct. Pennell, 737 F. 2d at 526. The theory was briefly considered in a recent unpublished opinion but found inapplicable to the facts in the case. United States v. Doss, 924 F. 2d 1059 (6th Cir.1991). Under this theory, due process requires an immunity grant where the prosecution abuses its discretion by intentionally attempting to distort the fact-finding process. Angiulo, 897 F. 2d at 1191. Immunity under this theory should not be granted lightly. Smith, 615 F. 2d at 968. The defendant must show “ ‘that the government’s decisions were made with the deliberate intention of distorting the judicial fact finding process.’ ” Id. (quoting United States v. Herman, 589 F. 2d 1191, 1204 (3d Cir.1978), cert. denied, 441 U.S. 913, 99 S.Ct. 2014, 60 L.Ed.2d 386 (1979)). Mohney contends that the government here deliberately withheld immunity in order to .keep necessary exculpatory evidence from the jury. It is clear that the government kept out important and relevant testimony of how the returns were prepared, including Mohney’s involvement. The prosecution, however, is only prevented from refusing to immunize a witness when the prosecution’s “sole desire” is to keep exculpatory testimony from the jury. Angiulo, 897 F. 2d at 1193. The prosecution may properly refuse to immunize a witness where it does not wish to hinder future criminal prosecutions of the witnesses. Id.

Mohney also argues that the government’s selective grants of immunity to its own witnesses, while denying immunity to his witnesses, deprived him of a fair trial. Selective grants of immunity could violate due process where they produce “ ‘egregiously lopsided access to evidence.’ ” Hooks, 848 F. 2d at 802-03 (quoting United States v. Buljubasic, 808 F. 2d 1260, 1268 (7th Cir.), cert. denied, 484 U.S. 815, 108 S.Ct. 67, 98 L.Ed.2d 31 (1987)); see also United States v. De Palma, 476 F.Supp. 775, 781 (S.D.N.Y.1979). A defendant, however, does not have a right to have his witnesses immunized simply because the prosecution relies on immunized witnesses to make its case. See United States v. Chagra, 669 F. 2d 241, 259 (5th Cir.), cert. denied, 459 U.S. 846, 103 S.Ct. 102, 74 L.Ed.2d 92 (1982); see also Hooks, 848 F. 2d 785.

[T]he balance between the government’s interest in prosecuting accused felons and the accused’s interest in presenting exculpatory and otherwise unobtainable evidence should not be inflexibly resolved by the fortuity that the government grants immunity to a particular witness in a particular case. If the government’s prosecutorial interest outweighs a defendant’s interest in presenting such evidence, ... then the government’s interest also outweighs any abstract concern with symmetry.

Chagra, 669 F. 2d at 259. The government had already indicted Tompkins, Scribner, and Klein and thus had a real and legitimate interest in prosecuting them. Although our circuit has not directly addressed the issue of selective immunity grants, we have noted problems with compelling the prosecution to grant immunity to potential defendants:

[T]he government as a practical matter may encounter great difficulty in satisfying the “heavy burden” of proving that its evidence against the witness is neither directly nor indirectly traceable to the immunized testimony ... [T]he government in almost all such cases would be constrained to curtail the cross-examination of the immunized witnesses in order to “narrow the scope of the testimony that the witness will later claim tainted his subsequent prosecution.”

Pennell, 737 F. 2d at 528 (quoting Turkish, 623 F. 2d at 775). In light of these concerns, we do not believe that selective immunity grants violated due process on these facts.

Because Mohney failed to establish that he was entitled to a judicially compelled immunity grant, even if our circuit were to recognize such a judicial power, we hold .that the district court properly refused to order the prosecution to grant immunity to Tompkins, Scribner, and Klein.

2.

Other Allegations of Unfairness

Mohney raises other allegations of prose-cutorial misconduct and judicial errors depriving him of a fair trial. First, he protests the district court’s refusal to give the missing witness instruction which he requested, although the court did give a missing witness instruction. Second, he objects on relevancy grounds to the prosecution’s references to the nature of his business and his illicit relationship with a seventeen-year-old female, and to the testimony of his former partner, Burton Gorelick, regarding a skim of profits with Mohney from theaters and bookstores. We find these remaining allegations wholly without merit.

B.

Motion to Suppress

Mohney argues that the district court erred in refusing to suppress evidence found during searches of MBS and OMI, IA’s predecessor. The government conducted these searches under the authority of three warrants: two authorizing the search of MBS and one authorizing the search of Entertainment World, another Mohney business located in the same building as OMI. On appeal, Mohney argues that the evidence should have been suppressed because the government failed to show probable cause and because the warrants failed to state with sufficient particularity the items to be seized. We need not reach these issues, however, as Mohney does not have standing to challenge these searches.

The “rights assured by the Fourth Amendment are personal rights, [which] ... may be enforced by exclusion of evidence only at the instance of one whose own protection was infringed by the search and seizure.” Simmons v. United States, 390 U.S. 377, 389, 88 S.Ct. 967, 974, 19 L.Ed.2d 1247 (1968), quoted in Rakas v. Illinois, 439 U.S. 128, 138, 99 S.Ct. 421, 427, 58 L.Ed.2d 387 (1978). In some circumstances, an officer of a corporation may be a “person aggrieved” by a corporate search and’ seizure and thus have standing to challenge the search. For example, in Henzel v. United States, 296 F. 2d 650 (5th Cir.1961), the appellant could challenge the search because he was the organizer, sole shareholder, and president of the corporation, who prepared much of the material seized from his office, where he spent the greater part of every working day. Where the documents seized were normal corporate records not personally prepared by the defendant and not taken from his personal office, desk, or files, in a search that was not directed at him personally, the defendant cannot challenge a search as he would not have a reasonable expectation of privacy in such materials. United States v. Britt, 508 F. 2d 1052, 1055 (5th Cir.), cert. denied, 423 U.S. 825, 96 S.Ct. 40, 46 L.Ed.2d 42 (1975). See also Williams v. Kunze, 806 F. 2d 594 (5th Cir.1986). Without a reasonable expectation of privacy in the seized materials, an officer may not challenge a search of the corporation:

When a man chooses to avail himself of the privilege of doing business as a corporation, even though he is its sole shareholder, he may not vicariously take on the privilege of the corporation under the Fourth Amendment; documents which he could have protected from seizure, if they had been his own, may be used against him, no matter how they were obtained from the corporation. Its wrongs are not his wrongs; its immunity is not his immunity.

Lagow v. United States, 159 F. 2d 245, 246 (2d Cir.1946), cert. denied, 331 U.S. 858, 67 S.Ct. 1750, 91 L.Ed. 1865 (1947), quoted in Britt, 508 F. 2d at 1055; cf. United States v. Salvucci, 448 U.S. 83, 91-93, 100 S.Ct. 2547, 2552-54, 65 L.Ed.2d 619 (1980). Moh-ney argues that he had a reasonable expectation of privacy because MBS’ and OMI’s offices were not open to the public. However, it is hard to see how Mohney could have a reasonable expectation of privacy in documents he claimed to be completely uninvolved in preparing and which were kept in offices he claimed to rarely visit. Nor were the searches targeted at “getting” Mohney; the searches were conducted as part of an arson investigation begun by Indiana officials. Mohney, then, did not have a reasonable expectation of privacy in the materials seized that would permit him to challenge the search warrants and thus the evidence seized during these searches was properly admitted.

C.

Summary Witnesses

The prosecution presented the testimony of two summary witnesses, IRS Agents Bednarczyk and Peterson. These witnesses attended the entire trial and reviewed the voluminous documents entered into evidence in order to calculate the amount of gross income and/or gross receipts un-derreported on IA’s and Mohney’s tax returns. Bednarczyk’s testimony addressed the corporate returns and Peterson testified as to the income underreported on the individual returns. Both used summary schedules which were admitted into evidence.

Mohney raises several objections to the testimony of Bednarczyk and Peterson. First, he argues that the district court erred in denying his motion to sequester Peterson during Bednarczyk’s testimony. Second, he submits that they should not have been allowed to use summary charts. Third, he contends that the summary witnesses should not have been given access to documents not provided to the defense and not submitted as evidence. Fourth, he contends that the trial court erred in allowing the summary witnesses to render opinions on the ultimate issue, whether funds were diverted.

1.

Exclusion of Witnesses

Federal Rule of Evidence 615 provides, in relevant part, that:

At the request of a party the court shall order witnesses excluded so that they cannot hear the testimony of other witnesses, and it may make the order of its own motion. This rule does not authorize exclusion of ... (3) a person whose presence is shown by a party to be essential to the presentation of the party’s cause.

Mohney moved to sequester Peterson under this rule so that Peterson, in testifying regarding the individual returns, would not “parrot” Bednarczyk’s calculations and testimony. Because Peterson’s testimony was based on Bednarczyk’s calculations, the court denied the sequestration request so that if cross-examination should bring out any facts not considered by Bednarczyk in making his calculations, Peterson would be present to ensure the accuracy and completeness of his own testimony.

The decision to permit a witness to remain in the courtroom “is within the discretion of the trial judge and should not normally be disturbed on appeal.” Morvant v. Construction Aggregates Corp., 570 F. 2d 626, 630 (6th Cir.), cert. dismissed, 439 U.S. 801, 99 S.Ct. 44, 58 L.Ed.2d 94 (1978). This court has recognized that

the presence in the courtroom of an expert witness who does not testify to the facts of the case but rather gives his opinion based upon the testimony of others hardly seems suspect and will in most cases be beneficial, for he will be more likely to base his expert opinion on a more accurate understanding of the testimony as it evolves before the jury. Id. at 629-30. Therefore, “where a fair showing has been made that the expert witness is in fact required for the management of the case, and this is made clear to the trial court, we believe that the trial court is bound to accept any reasonable, substantiated representation to this effect by counsel.” Id. at 630. The prosecution explained that the calculations of the individual returns depended on the calculations of the corporate returns and thus it would be beneficial for Peterson to hear Bednarc-zyk’s testimony. The court thus did not abuse its discretion in allowing Peterson to remain in the courtroom. However, even if the court had abused its discretion, Mohney failed to show that the asserted error “ ‘created sufficient prejudice to require reversal.’ ” United States v. Bobo, 586 F. 2d 355, 366 (5th Cir.1978) (quoting United States v. Warren, 578 F. 2d 1058, 1076 (5th Cir.1978) (en banc), cert. denied, 446 U.S. 956, 100 S.Ct. 2928, 64 L.Ed.2d 815 (1980)), cert. denied sub nom., Rowan v. United States, 440 U.S. 976, 99 S.Ct. 1546, 59 L.Ed.2d 795 (1979).

Mohney contends that the court should have sequestered Peterson because this court’s decision in United States v. Pulley, 922 F. 2d 1283, 1285-86 (6th Cir.1991), cert. denied, — U.S. -, 112 S.Ct. 67, 116 L.Ed.2d 42 (May 28, 1991), limits the government to designating only one agent-witness to represent it. Pulley, however, dealt with subsection (2) of Fed.R.Evid. 615 prohibiting the sequestration of “an officer or employee of a party which is not a natural person designated as its representative by its attorney.” Fed.R.Evid. 615. Because this case involves subsection (3) and because the prosecution established that both witnesses were “essential to the presentation of [its] cause” under that subsection, Pulley does nbt control.

2.

\

Flow Charts

Agent Bednarczyk used a chart as a visual aid in explaining how profits were skimmed. In commenting on such charts, this circuit has noted that “[tjhere is an established tradition, both within this circuit and in other circuits, that permits a summary of evidence to be put before the jury with proper limiting instructions.” United States v. Scales, 594 F. 2d 558, 563 (6th Cir.), cert. denied, 441 U.S. 946, 99 S.Ct. 2168, 60 L.Ed.2d 1049 (1979). Such a limiting instruction should explain “that the chart is not itself evidence but is only an aid in evaluating the evidence.” Id. at 564. The court here provided such an instruction. Before the chart was shown to the jury, the court cautioned that “this is generally known as a visual aid. It is not evidence at this point. It’s a visual aid to verbal testimony.” After the defense objected that the testimony based on the flow chart was improper as the jury would accept the facts shown in the chart as conclusively proven, the court once again reminded the jury that the chart served simply as the foundation for Bednarczyk’s calculations. Finally, the district court instructed the jury:

This witness has been qualified as an expert witness in the area of general accounting principals [sic] and knowledge of the Internal Revenue Code and the regulations under the Internal Revenue Code. He is not qualified of course to summarize testimony before you in this case. Therefore the diagram that you see before you is merely an explanation of his understanding of what the testimony has been with regard to the matters that are on that chart. It is not the subject of his expert testimony. It is the facts upon which his expert testimony is based.

To the extent that those facts you find not be established in this case then you will determine whether or not and what effect if any the fact that something has not been established or something on that chart is inaccurate affects his expert opinion, whether it does or it does not is a matter for you.... I just want to indicate that that is not evidence in this case. It’s merely before you as his understanding or the basis upon which he renders his opinion, his factual understanding of the flow.

Because the court instructed the jury very clearly that the flow charts were simply used to establish the basis of the calculations, it did not abuse its discretion in allowing their use.