Defendant Carl Nanni appeals from judgments entered in the United States District Court for the Western District of New York following a jury trial before Richard J. Arcara, Judge, convicting him on five counts of assisting in the preparation of false tax returns, in violation of 26 U.S.C. § 7206(2), and one count of conspiring to defraud the United States, in violation of 18 U.S.C. § 371. Nanni was sentenced principally to 32 months’ imprisonment, to be followed by three years’ supervised release. On appeal, he contends that he is entitled to dismissal of the indictment or, alternatively, a new trial and other relief, on the ground that his Fifth Amendment privilege against self-incrimination was violated by the government’s use against him of evidence derived from his immunized testimony before a state grand jury. For the reasons that follow, we disagree and affirm the judgment of conviction.
I. BACKGROUND
The present prosecution focused principally on Nanni and his codefendant Saverio T. Latin, who pleaded guilty to various offenses and testified against Nanni at trial. The events in question date back to the early 1980’s when New York State (“State”) prosecutors were investigating and prosecuting an “adult entertainment” business called “Good Time Charlies” for state-law obscenity offenses. Latin had been president of a company that owned Good Time Charlies; Nanni was his accountant. Most of the events pertinent to the present appeal do not appear to be in substantial dispute.
A. The 1983-1984 State Grand Jury Proceedings
On three occasions in 1983-1984, Assistant District Attorney George Burgasser ques*1428tioned Nanni before a grand jury in Niagara County, New York (the “State grand jury”), investigating possible violations by Good Time Charlies (sometimes referred to as “GTC”) of State obscenity laws. Nanni testified that he served as accountant to DiHar, Inc., the former corporate owner of GTC, and to Latin, DiHar’s owner. Nanni also stated that he provided accounting services to AJS Merchandising, Inc. (“AJS”), which had purchased GTC from DiHar; Nanni stated that he had notarized the signature of AJS’s owner, John Sureaz, on certain corporate papers. In addition, Nanni testified that he was responsible for writing most of the cheeks for GTC under each of its owners, that he possessed a stamp reproducing the signature of John Sureaz, and that he used the signature stamp at Sureaz’s instruction.
On several issues Nanni gave apparently inconsistent testimony relating to Sureaz. At one point, he described Sureaz as weighing between 160 and 175 pounds, while at another, he described Sureaz as between 135 and 140 pounds. As to how he came into possession of the Sureaz signature stamp, Nanni first testified thát Sureaz had brought the stamp without Nanni’s office having either requested or ordered it, but later testified that Nanni’s office had ordered the stamp. Nanni also testified that Sureaz would often come to the office and not speak with Nanni, the only accountant with whom Sureaz dealt, and would just leave messages with “[ajnybody.” (Transcript of Grand Jury Testimony of Carl Nanni, dated January 9, 1984, at 28.)
During one exchange, Burgasser noted the apparent inconsistency between the supposedly close business relationship between Nanni and Sureaz and the paucity of Nanni’s information about Sureaz:
Q: Have you ever observed the vehicle he drives?
A: No sir.
Q: Ever see a plate number on the car?
A: No sir.
Q: Have you ever turned around and asked him for any further personal information other than what you’ve told us before?
A: Yes, I’ve asked him, that the end of the year’s coming, I have to have all the old records back to complete tax returns, otherwise my hands are tied, I just can’t do it.
Q: Okay. Has Mr. Sureaz ever told you his home address so you can contact him?
A: He gave me one address.
Q: Have you ever tried contacting him at that address.
A: No sir, no sir.
Q: Has he left you a phone number?
A: No sir.
Q: Let me ask you this. You’re keeping very important records for this individual, correct?
A: No sir, I’m only keeping payroll records.
Q: Doesn’t he also leave the stamp with you to stamp checks?
A: Yes sir, he does.
Q:, Okay, and doesn’t he also leave the checkbook with you?
A: Yes sir.
Q: But he doesn’t leave you any information as to how to contact him, if it becomes necessary?
A: No sir, he says he would contact me....
(Id. at 22-23.) Later, Burgasser returned to this theme:
Q: Now, him giving you that rubber stamp, would that be, in your estimation, a great trust in yourself?
A: Most accountants you have great trust in.
Q: But yet he doesn’t have trust in you to leave a phone number where you can contact him?
(Id. at 26-27.) Nanni’s answer was unresponsive. Eventually, Burgasser asked Nanni directly whether he had “ever verified that this man in fact is a person known as John Sureaz?” to which Nanni responded: “No sir, because normally accountants verifying — if you come in the office, say you’re John Doe, we just take it as your word.” (Id. at 33-34.) *1429Burgasser came to believe that Latin was still involved in Good Time Charlies despite its purported sale to AJS, and that Sureaz did not exist. Although this belief was initially kindled by Nanni’s immunized grand jury testimony, Burgasser as the trial assistant had developed numerous other sources. After causing Sureaz’s indictment, the district attorney’s office had made extensive efforts to find him so as to arrest him for trial. The futility of those efforts to find Sureaz, together with trial evidence, fortified Burgasser’s belief in Sureaz’s non-existence.
Nanni last appeared before the State grand jury on January 9, 1984. Under New York law, he was automatically granted immunity, with very limited exceptions, for his testimony in all of his grand jury appearances. See N.Y.Crim.Proc.Law § 190.40.
B. The 1987-1992 Federal Tax Investigations
In 1987, the Internal Revenue Service (“IRS”) began an investigation of Latin’s income tax returns. This investigation was initially conducted as a civil inquiry by IRS agent Barbara Ricotta. Rieotta first contacted Burgasser about the earlier obscenity prosecution of Good Time Charlies. She learned from Burgasser that Sureaz, though indicted, had not appeared in the proceedings, and that Burgasser believed Latin to be still involved in GTC and Sureaz to be fictitious.
Although Ricotta received a transcript of the State grand jury proceedings, she did not read it but instead destroyed it so that it could not taint her investigation. Her independent investigation, discussed in greater detail in Parts II.B.l and 2. below, included meetings with Nanni, Latin’s attorney Robert Zueco, GTC employee Brian Laraby, and employees of the bank at which AJS had its account. She also attempted to meet with Sureaz but was unable to locate him. In a report on her investigation, Ricotta concluded that Latin continued to own GTC and that he was part of “a conspiracy involving at least Latin, Nanni, Zueco and Laraby” to skim money from the operations at GTC without reporting it as income. Rieotta recommended that IRS’s Criminal Investigation Division (“CID”) commence a fraud investigation.
The ensuing criminal investigation was led by IRS agent Michael DelValle, assisted by agents of the Federal Bureau of Investigation (collectively the “government agents”). DelValle read Ricotta’s report. He also learned that the grand jury materials from the obscenity investigation had been made public, and he obtained and read those materials, including Nanni’s grand jury testimony. As discussed in greater detail in Part II.B.3. below, DelValle had in mind, and to an extent used, both Ricotta’s report and Nanni’s grand jury testimony in pursuing his investigation.
In November 1989, DelValle applied to the CID Chief and other IRS officials (collectively the “CID managers”) for permission to conduct an undercover operation. His application emphasized his belief that. Sureaz did not exist and that Latin was the true owner of AJS. Permission was granted in January 1990, and undercover government agents, deployed to pose as prospective purchasers of Good Time Charlies, recorded conversations that strongly supported Ricotta’s conclusions as to the existence' of a money-skimming tax fraud conspiracy.
In July 1990, the government applied for search warrants for Good Time Charlies and Nanni’s accounting firm. The warrant application was supported by DelValle’s affidavit, which included an extensive summary of the information gained through the undercover operation and stated DelValle’s belief that Sureaz did not exist. In support of that belief, the affidavit stated that searches of records of, inter alia, IRS, the Social Security Administration, and all state departments of motor vehicles had revealed no reference to any person by the name of John Sureaz. The affidavit also made explicit references to Nanni’s grand jury testimony as support for DelValle’s belief that Sureaz did not exist. The warrants were issued, and the ensuing search of GTC uncovered various business records, as well as the John Sureaz signature stamp. In addition, a federal grand jury-subpoenaed various individuals associated with Good Time Charlies to compel them to *1430provide handwriting exemplars. Nanni was among those subpoenaed.
C. The Present Indictment and the Kastigar Ruling
The federal grand jury returned an indictment in 1992 charging Nanni and Latin, along with Latin’s wife and stepson, with conspiracy to defraud the United States and several counts of preparing and filing false tax returns. Nanni moved to dismiss the indictment against him or to suppress evidence, arguing that the government had made improper use of his immunized State grand jury testimony. He contended that the government’s investigation emanated from the belief that Sureaz was a fictitious person used for purposes of tax evasion and that .Nanni’s grand jury testimony played a major role in . the formation of DelValle’s belief that Sureaz did not exist. Nanni’s motions were referred to Magistrate Judge Edmund F. Maxwell for a hearing pursuant to Kastigar v. United States, 406 U.S. 441, 92 S.Ct. 1653, 32 L.Ed.2d 212 (1972) (“Kastigar ”), and for a report and recommendation.
At the Kastigar hearing, as explored in greater detail in Part II.B. below, Ricotta, DelValle, and other witnesses testified as to, inter alia, (a) the extent of the investigating agents’ exposure to Nanni’s immunized testimony, and (b) the decisionmaking process by which they drew certain conclusions and determined to pursue various lines of inquiry. The government’s documentary evidence included Ricotta’s report, DelValle’s applications for undercover operations, and DelValle’s affidavit in support of the search warrants. The government also presented the court with a list indicating the source of each item of proposed trial evidence, comprising, inter alia, tax returns in the files of IRS, bank statements and canceled checks obtained from AJS’s bank, state motor vehicles department certifications as to the lack of any record for a John Sureaz, and other evidence developed in the course of the investigation. The list included the handwriting exemplars provided by Nanni pursuant to the grand jury subpoena; numerous items seized in the execution of the search warrants, including the Sureaz signature stamp, a Zueco letter to Nanni with regard to the need for a Sureaz signature, and other documents specifically referring to Sureaz.
In a Report and Recommendation dated October 21, 1993, the magistrate judge recommended that Nanni’s motions be denied. He found that Ricotta had not read the State grand jury minutes and that her report and conclusions were based on legitimate independent sources. Emphasizing the many steps that the government, including Ricotta, had undertaken to locate Sureaz without success, and DelValle’s reliance on Rieotta’s independent investigation, the magistrate judge credited DelValle’s testimony that he had not impermissibly used the grand jury testimony. Further noting that Sureaz would not figure prominently in the government’s case against Nanni, the magistrate judge also concluded that if there had been an impermissible use of Nanni’s grand jury testimony, the error was minor and nonpervasive. He found that the testimony had been used, at most, in DelValle’s search warrant application affidavit, and even there only to corroborate other facts indicating Sureaz’s nonexistence.
The district court adopted the recommendation of the magistrate judge. The case was tried, with the challenged evidence admitted. As a result of the handwriting exemplars, a handwriting expert identified Nanni as the writer of two “Sureaz” signatures. The jury found Nanni guilty on all counts, and he was sentenced as indicated above. This appeal followed.
II. DISCUSSION
On appeal, Nanni argues that the government’s investigation was spawned by its belief, originating in his immunized grand jury testimony, that Sureaz did not exist, and that the government impermissibly used that testimony in obtaining the tape recordings made during the undercover operation, his handwriting exemplar, and the evidence seized pursuant to the search warrants. We reject' the contentions that the immunized. testimony was used in obtaining the tape recordings and the handwriting exemplar; and although we reach the contrary conclusion with respect to the search warrants, we *1431conclude that that error was harmless because the use of Nanni’s testimony in the search warrant application was not a significant factor in either the decision to seek or the decision to issue the warrants.
A. Principles Governing Use of Immunized Testimony
The government may compel an individual to give seh-incrirriinating testimony only by granting him an immunity that is at least as extensive as the privilege against self-incrimination conferred by the Fifth Amendment. See, e.g., Kastigar, 406 U.S. at 449, 92 S.Ct. at 1658-59. Since the Fifth Amendment protects the witness against “ ‘the use of his testimony to search out other testimony to be used in evidence against him,’” as well as against the prosecution’s gaining from the testimony “ ‘a knowledge of the details of a crime, and of sources of information which may. supply other means of convicting the witness,”’ id. at 454, 92 S.Ct. at 1661 (quoting Counselman v. Hitchcock, 142 U.S. 547, 564, 586, 12 S.Ct. 195, 198, 206, 35 L.Ed. 1110 (1892)), the statutory immunity, to be sufficient to supplant the constitutional protection, must “prohibit[ ] the prosecutorial authorities from using the compelled testimony in any respect,” including both use of the compelled testimony itself and the use of “evidence derived directly and indirectly therefrom.” Kastigar, 406 U.S. at 453, 92 S.Ct. at 1661 (emphasis in original). This immunity not only prohibits use against the witness of his truthful testimony that is self-inculpatory, but also, except to the extent that the testimony amounts to perjury, see, e.g., United States v. Apfelbaum, 445 U.S. 115, 127-28, 100 S.Ct. 948, 955-56, 63 L.Ed.2d 250 (1980), prohibits the use of negative inferences drawn from his false testimony which, if believed, would tend to exculpate him, see, e.g., United States v. Hinton, 543 F.2d 1002, 1009 (2d Cir.), cert. denied, 429 U.S. 980, 97 S.Ct. 493, 50 L.Ed.2d 589 (1976). A state immunity statute containing such prohibitions protects the witness from the use of his testimony by federal, as well as state, authorities. See Murphy v. Waterfront Commission, 378 U.S. 52, 77-78, 84 S.Ct. 1594, 1608-09, 12 L.Ed.2d 678 (1964).
This “use” immunity is to be contrasted with “transactional” immunity, which protects a witness from prosecution for the offense to which the compelled testimony relates. The Fifth Amendment itself does not confer transactional immunity, and an immunity statute thus need not confer transactional immunity in order to pass constitutional muster. See, e.g., Kastigar, 406 U.S. at 453, 458-59, 92 S.Ct. at 1661, 1663-64; Murphy v. Waterfront Commission, 378 U.S. at 77-79, 84 S.Ct. at 1608-10 (Fifth Amendment protects a state witness only against the “use of compelled testimony and its fruits” by the federal government rather than against federal prosecution under federal law altogether). Further, a state statute that grants transactional immunity does not bar the federal government from prosecuting the witness, so long as the federal government can show that it has not used the immunized testimony. See United States v. DeSalvo, 26 F.3d 1216, 1221 (2d Cir.) (“testimony given under a state grant of transactional immunity earns only use immunity in a federal court”), cert. denied, — U.S. -, 115 S.Ct. 192, 130 L.Ed.2d 124 (1994).
The government’s direct use of immunized testimony by, for example, presenting it at a trial of the witness who gave it or by referring to it in an application for court authorization to obtain evidence against the witness, is plainly a violation of the witness’s Fifth Amendment rights. See, e.g., United States v. Pelletier, 898 F.2d 297, 303 (2d Cir.1990) (use at trial or before grand jury); United States v. Gallo, 859 F.2d 1078, 1082 (2d Cir.1988) (use in wiretap application) (opinion of Winter, J.), cert. denied, 490 U.S. 1089, 109 S.Ct. 2428, 104 L.Ed.2d 986 (1989); see also id. at 1094-95 (opinion of Altimari, J., dissenting). Where the witness asserts that the government has used the immunized testimony less directly, as, for example, a lead that turned up other evidence against the witness, the inquiry into whether there has been a violation becomes more complicated. Once the defendant shows that, under a grant of immunity, he has testified to matters related to the prosecution, the government has the burden of proving by a preponderance of the evidence *1432that no violation occurred. See, e.g., United States v. Schmidgall, 25 F.3d 1523, 1528 (11th Cir.1994); United States v. Harris, 973 F.2d 333, 336 (4th Cir.1992); United States v. Overmyer, 899 F.2d 457, 462-63 (6th Cir.), cert. denied, 498 U.S. 939, 111 S.Ct. 344, 112 L.Ed.2d 308 (1990). The burden is a “heavy” one, Kastigar, 406 U.S. at 461, 92 S.Ct. at 1665, because it “is not limited to a negation of taint; rather, it imposes on the prosecution the affirmative duty to prove that the evidence it proposes to use is derived from a legitimate source wholly independent of the compelled testimony,” id. at 460, 92 S.Ct. at 1664-65; see also Murphy v. Waterfront-Commission, 378 U.S. at 79 n. 18, 84 S.Ct. at 1609 n. 18. Neither a mere “assertion that the immunized testimony was not used” nor even proof that the prosecutor “had no direct or indirect access to the grand jury minutes” is sufficient. United States v. Nemes, 555 F.2d 51, 55 (2d Cir.1977).
Although the prosecution’s burden is heavy, it is not insurmountable. The government need not show that the prosecution team had no exposure to the immunized testimony at all. See, e.g., United States v. Catalano, 491 F.2d 268, 272 (2d Cir.) (rejecting the suggestion “that access to grand jury testimony ipso facto prevents the government from carrying its burden under Kastigar ”), cert. denied, 419 U.S. 825, 95 S.Ct. 42, 42 L.Ed.2d 48 (1974). While the strongest proof that the information came from an independent source would be evidence that the government was in possession of independent leads or evidence prior to the giving of the immunized testimony, see, e.g., United States v. Rivieccio, 919 F.2d 812, 815 (2d Cir.1990), cert. denied, 501 U.S. 1230, 111 S.Ct. 2852, 115 L.Ed.2d 1020 (1991), evidence that was obtained subsequent to the agent’s exposure to the immunized testimony can suffice to support a finding that the information was derived from independent sources, see, e.g., United States v. Fisher, 700 F.2d 780, 784 (2d Cir.1983). In determining whether the immunized testimony could have influenced the government’s decision to pursue its line of investigation, if it appears that that pursuit could have been motivated by both tainted and independent factors, the court must determine whether the government would have taken the same steps “entirely apart from the motivating effect of the immunized testimony.” United States v. Biaggi, 909 F.2d 662, 689 (2d Cir.1990) (citing Mt. Healthy City School District Board of Education v. Doyle, 429 U.S. 274, 97 S.Ct. 568, 50 L.Ed.2d 471 (1977)), cert. denied, 499 U.S. 904, 111 S.Ct. 1102, 113 L.Ed.2d 213 (1991). In United States v. Fisher, for example, the defendant had given local authorities information regarding firearms trafficking, after eliciting promises that he would not be prosecuted by them and that his information would not be turned over to federal authorities; his statement was nonetheless forwarded to a federal agent, Varriale. Thereafter, in an unrelated event, Fisher was arrested at the New York/Canada border carrying a gun, and another federal agent, Duquennois, routinely forwarded Fisher’s name and other information to Varriale. We held that the government had adequately shown that evidence uncovered in Varriale’s subsequent investigation had an independent source because
Varriale testified that the referral from Duquennois alone would have caused him to undertake his investigation. Once Fisher had been arrested, the evidence against him was compiled in a routine fashion that would inevitably have led to Fisher’s discovery____
Thus, we agree with the district court which found that the evidence offered by the Government in support of Fisher’s conviction was “derived from sources independent, in any event, from the statements made by the defendant to [a local agent]”
Because the discovery of Fisher’s crimes was inevitable once he was arrested at the border with a gun purchased in Vermont, any assurance he received from [the local authorities] becomes irrelevant since it would not have saved Fisher from federal investigation.
700 F.2d at 784.
If the court, finds that the government failed to establish by a preponderance that it did not use the immunized testimony, thus requiring the conclusion that *1433there has been Fifth Amendment violation, the appropriate relief will vary with the circumstances; but no relief should be granted if the government establishes beyond a reasonable doubt that the violation was harmless, see, e.g., United States v. Pelletier, 898 F.2d at 303; United States v. Gallo, 859 F.2d at 1083 (opinion of Winter, J.); id. at 1090 (opinion of Van Graafeiland, J., concurring). For example, if the government has presented immunized testimony to the grand jury, the indictment should be dismissed unless the government establishes that the grand jury would have indicted even absent that testimony. See, e.g., United States v. Rivieccio, 919 F.2d at 816 n. 4; United States v. Pelletier, 898 F.2d at 303. If the government has presented immunized testimony to some other decisionmaker, such as a judge from whom a wiretap authorization is sought, the court should invalidate the decision and suppress the evidence unless the testimony presented “was so inconsequential ... that it could not have influenced the government’s decision to seek or the district judge’s decision to issue the surveillance order.” United States v. Gallo, 859 F.2d at 1079 (opinion of Winter, J.); see also id. at 1091 (opinion of Van Graafeiland, J., concurring). If the government has not presented the grand jury with immunized testimony but has presented evidence obtained through the use of such testimony, the indictment is not to be dismissed, but the court should suppress the evidence. See, e.g., United States v. Rivieccio, 919 F.2d at 816. If the court has failed to exclude tainted evidence at trial, we will order a new trial unless we are persuaded beyond a reasonable doubt that the jury would have reached the same verdict even without consideration of the tainted evidence. See United States v. DeSalvo, 26 F.3d at 1223.
In determining whether a magistrate’s decision to authorize the seizure of evidence was influenced by the presence of improper material in the application, the court “must examine the unchallenged portions of the affidavit and determine whether those portions are sufficient to support a probable cause finding.” United States v. Gallo, 859 F.2d at 1084 (opinion of Winter, J.); see generally Franks v. Delaware, 438 U.S. 154, 171-72, 98 S.Ct. 2674, 2684-85, 57 L.Ed.2d 667 (1978). Whether the untainted portions suffice to support a probable cause finding is a legal question, and we review the district court’s ruling on that question de novo. See, e.g., United States v. Smith, 9 F.3d 1007, 1011 (2d Cir.1993). Whether the government made use of immunized testimony, and, if it did, whether it would have taken the same steps entirely apart from the motivating effect of the immunized testimony, are questions of fact, and the district court’s findings on those questions will be affirmed unless they are clearly erroneous. See United States v. Rivieccio, 919 F.2d at 814.
With these principles in mind, we turn to the question of whether the evidence presented at the Kastigar hearing in the present case supports the district court’s rulings.
B. The Evidence at the Kastigar Hearing
At the outset, we note that notwithstanding Nanni’s attorney’s attempt to learn “what types of sources, if any, the government had for the evidence that they’re using against Mr. Nanni other than his grand jury testimony” (Kastigar Hearing Transcript, June 18, 1993 (“June 18 Tr.”), at 5), the Assistant United States Attorney (“AUSA”) did not appear to have fully comprehended the government’s burden to prove affirmatively that its proposed trial evidence had legitimate sources wholly independent of Nanni’s grand jury testimony, and that the government could not carry that burden by merely asserting that his testimony had not been used.
The government began its presentation at the Kastigar hearing by calling DelValle as a witness and subjecting him to a brief and superficial examination. In his direct examination, DelValle testified that he received Ricotta’s report in September 1988, reviewed it, and did some investigating of his own in October 1988, including reviewing Nanni’s grand jury testimony. He testified that “as a result of that” he prepared in December 1988 a summary evaluation recommending that the matter be pursued. DelValle then testified as follows:
Q. And as a result of the review of the grand jury testimony, did you use any of *1434that testimony for any investigative lead or any investigative purpose?
A. No, I did not.
Q. However, did you include cross reference to the contents of that grand jury testimony in the search warrant application which was made in July of 1990?
A. Yes, I did.
Q. And what was the purpose of that reference in the affidavit?
A. To note inconsistencies in the existence of John Sureaz.
(June 18 Tr. at 19-20). The AUSA stated -that he had no further questions of DelValle. His direct examination occupies just four pages of transcript.
It later became clear that the government, which apparently had planned to call no other witnesses, believed this testimony sufficed to carry its burden. Thus, although the court stated, “As I understand it under Kastigar, the government has the affirmative duty to prove that the evidence it proposes to use is derived from a legitimate source wholly independent of the compelled testimony” (June 18 Tr. at 106), the AUSA stated his view that “the only real issue is what documents were obtained as a result of that Niagara County grand jury testimony. The agent said none. It was his direct testimony. So period” (June 18 Tr. at 111).
Had there been no other testimony, we are confident that the district court would have concluded that the government had not carried its burden. However, the hearing did not end with DelValle’s direct testimony. DelValle was subjected to additional examination (some helpful to the government, some helpful to the defense), and the government eventually called other important witnesses, including Ricotta. We review all of the evidence adduced at the Kastigar hearing, including that elicited on cross-examination of the government’s witnesses, to determine whether the district court’s rulings are adequately supported.
1. Sources Used by Ricotta
Ricotta testified that she had been given responsibility for a field investigation of Latin in April 1987. The assignment resulted from an in-office audit of Latin. Ricotta first encountered Nanni’s name in connection with this assignment because following IRS’s initial audit letter to Latin, Nanni had responded with a letter from Latin giving Nanni power of attorney to represent him in the audit. The office file Ricotta received contained no grand jury materials.
At the outset of her investigation, Ricotta recalled that there had been an obscenity prosecution of Latin; she learned that the trial had been conducted by Burgasser, and she spoke to him two or three times by telephone.
Q. ... [W]hat was the content of those telephone conversations?
A. Well, the essence would be that Burgasser did not believe that Sureaz existed.
Q. Did Mr. Burgasser indicate to you that he had any evidentiary — that he had some evidence that indicated that that was the ease?
A. Just generally from all the evidence that had come forth in the trial and that Sureaz never appeared.
Q. And it was based upon those facts and that lack of — or the evidence at trial, at the pornography trial, that it was based upon that that Mr. Burgasser gave you his opinion—
A. That’s correct.
Q. —that Mr. Sureaz did not exist?
A. That’s correct.
(Kastigar Hearing Transcript, July 23, 1993 (“July 23 Tr.”), at 30-31.) Ricotta did not recall that Burgasser ever referred to Nanni or any accountant for Good Time Charlies.
Burgasser told Ricotta that he had previously given some materials (whose nature he did not describe to Ricotta) to IRS Agent Richard E. Rozicki, an agent in CID, and Ricotta contacted Rozicki to obtain those materials. Rozicki, who also eventually testified at the Kastigar hearing but apparently had no role in the present investigation or prosecution, had conducted a brief probe into Good Time Charlies in 1984 as part of an investigation of “anything that had potential for crimi*1435nal- tax violations” in the Niagara County area. (July 23 Tr. at 57.) During that investigation, Rozicki contacted Burgasser; Rozicki did not recall that Burgasser had ever opined to him that Sureaz did not exist or had ever mentioned Nanni’s name. Burgasser obtained a court order permitting disclosure of the State grand jury materials to Rozicki, and Rozicki read the materials, including Nanni’s testimony. Rozicki attempted to determine who owned Good Time Charlies, checking county records with respect to ownership of property, other public records, and internal IRS records. His attempts “showed no existence of a Sureaz.” (Id. at 72.) Three years later, Rozicki turned his entire file, including the grand jury materials, over to Ricotta and “closed [the matter] out.” (Id. at 60.) He kept no copies. He did not remember having any conversation with Ricotta, though he thought it was possible that he might have opined, as a result of his own efforts to locate Sureaz, that Sureaz did not exist.
When Ricotta received Rozicki’s file, she noticed that it bore a sticker indicating that the file contained grand jury materials. Because IRS audit guidelines state that grand jury materials should not be used, Ricotta did not read any part of Rozicki’s file, but instead shredded it:
Q. So you recall seeing something marked grand jury?
A. Right.
Q. You don’t recall whose testimony it might have been?
A. I have no- idea.
Q. Did you — did you look inside the pages at all? Did you read any of the pages of those grand—
A. I read nothing. I saw the sticker on the first page. I flipped a few comers, saw that they had stickers, I didn’t go any further. I didn’t want to have anything that would taint my examination at all.
Q. And what did you do with it?
A. I disposed of it.
The Court: You what?
The Witness: Disposed of it.
By Mr. Littlefield [AUSA]:
Q. How did you dispose of it?
A. Our policy is if something is not going with the case file, for protection of the taxpayers, we shred them—
Q. Did you shred them?
A. —so they wouldn’t be disclosed. Yes, I did.
The Court: When you got these materials from Mr. Rozicki, did you receive any other materials at the same time, anything other than this grand jury—
The Witness: ... I’m not sure. Because when I saw those on the front, and I was hyper about not working with anything that I shouldn’t have, I really did not look through them to see if there was anything that was usable, so it’s a possibility. I don’t know.
The Court: When you decided to dispose of them, did you check with anybody else to see if other copies were available to other people before you shredded what you had?
The Witness: No.
(July 23 Tr. at 17-18, 51.) Ricotta shredded them “personally.” (Id. at 19.) Since she did not look at the grand jury materials, she did not know whether or not Nanni’s testimony was included.
Rieotta’s ensuing investigation included interviewing Nanni because Nanni had Latin’s power of attorney. She testified that, as refleeted in her 1988 referral report (“Referral Report” or “Report”) to the criminal division, she had received various documents from Nanni.
2. Information Turned up in Rieotta’s Investigation
After approximately a year-long investigation, Ricotta sent her Report to CID, indicating that Latin had fraudulently failed to report sizeable amounts of income on his tax returns. The Report posited that for the years 1983, 1984, 1985, and 1986, Latin had fraudulently omitted income of $55,951, $43,-970, $50,564, and $20,200, -respectively.
Ricotta’s Report reflected her interviews with Burgasser and numerous other individuals, including Nanni, Latin, Zueco, Laraby, *1436bank employees, and a confidential informant. As to the financial machinations, she learned from Zueco that in 1982 Latin had purchased the braiding in which Good Time Charlies was housed for $175,000; she concluded that the rent on the braiding reported by Latin and deducted by AJS for 1986— $96,000 — was excessive. Ricotta also learned from bank records that large amounts of cash brought to the bank by Latin and other Good Time Charlies employees, as reflected in the bank’s currency transaction reports, did not show up in Good Time Charlies’ account. For example, during one seven-month period Latin’s son or son-in-law was issued currency transaction reports totaling $93,844, but made deposits of only $32,313.
Ricotta also spoke with State sales tax investigator John Costello, who similarly had examined some of AJS’s banking records and determined that there was missing income. Apparently, Latin’s attorney Zueco had indicated to Costello that Sureaz had been paid dividends. However, Costello, did not believe Sureaz existed since he had tried to get from Zueco information as to Sureaz’s whereabouts or Social Security Number, but had had no success.
Though Latin claimed to have sold Good Time Charlies to Sureaz in 1982, Ricotta learned that he continued to perform owner-type duties thereafter. He personally made at least one sizeable cash deposit into AJS’s bank account. Further, a confidential informant who worked at GTC from February 1986 through November 1987 informed Ricotta that for part of that period Laraby ran GTC’s day-to-day operations and that Latin came to GTC periodically and would have Laraby get the business books for Latin to review; if Laraby was not there, Latin would have the informant get the books. Latin gave Laraby instructions on making bank deposits, making payments to Zueco, and paying other bills. The informant said he had never heard of Sureaz.
. Ricotta interviewed Laraby in the presence of Zueco, questioning Laraby as to GTC’s financial methods. Laraby said that GTC was a strictly cash business; income was put in the safe, and “[s]omeone” would pick up the money. During Ricotta’s first interview with Laraby, Zueco gave her copies of the GTC checking account statements; but when asked for any other accounts or items to reconcile those balances with other records, “Zueco had no answer.” Zueco said bank statements were sent to him, and he believed that through 1986, checks were being made out by Nanni. The Report stated: “It became apparent as the examination proceeded, that the checks disbursed from the business account of AJS ... were being written by Nanni, at least thru the end of 1986, and a rubber stamp with a signature of John Sureaz was imprinted for the signature.”
In Ricotta’s first interview with Laraby, he said he had seen Sureaz once, in 1986, but had never had contact with him. In a later interview, Laraby said he thought he had seen Sureaz once, in 1983, but had never met him.
Ricotta interviewed Latin, also in the presence of Zueco, as to Latin’s dealings with Sureaz. Latin said that he had not known Sureaz before selling GTC to him and leasing to Sureaz the building in which GTC was operated. He said he had checked Sureaz out with some “vendors”; but he refused to identify the vendors to Ricotta. Latin did no other credit check of Sureaz, and he stated that he never knew Sureaz’s address. Zueco said he assumed Sureaz lived in Rochester since Sureaz would leave materials at Nanni’s Rochester office.
Ricotta received from Zueco a copy of the building lease, signed by Latin and Sureaz, and AJS’s application to do business in,New York State, signed by Sureaz and notarized by Nanni. Ricotta discussed with Zueco getting in touch with Sureaz to set up an appointment. Zueco responded that there was no way of getting in touch exeept by leaving correspondence “at the business.” Ricotta sought to make an appointment to go there but never received a response.
Before talking to Latin himself, Ricotta had tried to obtain work papers for Latin’s returns from Nanni. Though she did not ask for AJS records and though Nanni had said Latin had no connection with AJS, Nanni nonetheless produced AJS records in response to her request for records of Latin. *1437The AJS tax returns bore a Sureaz signature; none of them revealed a Social Security Number for Sureaz. The returns for 1983 and 1984 bore Sureaz’s stamped signature; the 1986 return bore a handwritten Sureaz signature that Eicotta viewed as forged and possibly written by Nanni. At the Kastigar hearing, Eicotta, testified that she had reviewed numerous tax returns prepared by Nanni and was familiar with his handwriting. Her Eeport stated that she recognized Nanni’s handwriting on AJS’s 1985 return as well, though he was not listed as preparer.
When Eicotta interviewed Nanni, she asked how he contacted Sureaz. Nanni stated that Sureaz would leave records at Nanni’s office and then come back to pick up the tax return. When Eicotta asked why none of the returns prepared for Sureaz revealed Sureaz’s Social Security Number, Nanni said he had simply told Sureaz to enter that information.
Eicotta’s Eeport concluded:
It is my opinion that there is a conspiracy involving at least Latin, Nanni, Zueco and Laraby. The money has gone out of the business and supposedly no one can explain. It would appear that Latin still owns the business, GTC. He owns the building, his son or son-inlaw [sic] took care of the business transactions until 2/87 and made a deposit in 1984 after he had supposedly transferred the business. All attempts have been made to locate Sureaz to no avail. It is noted that since my first contact regarding the examination' of Latin’s return, no one has indicated that they have had contact with Sureaz.
The Eicotta Eeport thus demonstrated a thorough investigation, including interviews of numerous people who made' revealing statements, and the acquisition of material documents from Nanni, Zueco, AJS’s bank, and official files. We conclude that Eicotta’s testimony as to her immediate shredding of the grand jury material without reading it, and the evidence as to the information she obtained in her investigation were ample to support the district court’s finding that Eicotta had wholly independent sources for the conclusions she drew as to the nonexistence of Sureaz and the role of Nanni in the perceived fraudulent tax scheme.
Although at the start of her investigation Eicotta received Burgasser’s partially tainted suggestion that Sureaz did not exist, she would certainly have reached the same conclusion even absent any contact with Burgasser. The commencement of the field investigation had nothing to do with Nanni’s testimony. The very suspect circumstances surrounding Latin’s supposed sale of GTC and Nanni’s volunteering of AJS’s returns when only Latin’s were requested, would surely have caused Eicotta to take the further investigative steps that showed Latin to be still in control of GTC.
3. The Sources Used by DelValle
The sources used by DelValle are more problematic, for, as indicated above, he, unlike Eicotta, did read Nanni’s grand jury testimony. Thus, in his initial summary evaluation of Eicotta’s referral, in which DelValle quoted extensively from her Eeport and- described her conclusions, his description of his own visit to the Niagara County District Attorney included the following:
In several meetings with Peter Broderick, the District Attorney of Niagara County, I was able to obtain information relative to grand jury testimony____ Nanni testified before the grand jury that he had met John Sureaz and that Sureaz had signed documents in front of him and that he had notarized those documents for the incorporation of the business. He further stated that Sureaz had signed a rubber stamp for him and had given him complete authority as far as paying bills and using the rubber stamp. Nanni stated that he had met Sureaz on at least two occasions; one when he had him sign the forms and another was approximately one year later in his office.
Accordingly, inquiry was required into whether DelValle had legitimate wholly independent source's for the decisions made at several critical jimetures, to wit, those with respect to (1) whether to pursue the criminal investigation, (2) whether to pursue Nanni as a target of that investigation, (3) whether to request a handwriting exemplar from Nanni, (4) whether to conduct the undercover opera*1438tion, and (5) whether to utilize search warrants. The first two decisions entail inquiries that differ somewhat from the last three, for the first two focus solely on decisions by DelValle, whereas the last three require consideration also of decisions by other persons as to the methods DelValle would be allowed to use in pursuing the investigation. Thus, while the first two inquiries focus on DelValle’s thought processes, the last two focus in addition on what he communicated to other decisionmakers and on what factors influenced those other persons.
With respect to most of these decisions, and especially the first two, i.e., whether to investigate and whether to investigate Nanni, we have little difficulty in upholding the district court’s finding that there was no improper use of Nanni’s grand jury testimony. DelValle had begun by reviewing Ricotta’s Referral Report, which was purged of any initial taint and which amply spelled out the need for further investigation of several individuals, including Nanni. The Report revealed, inter alia, that there was strong evidence that $170,000 in cash had gone unreported, that Nanni had check-writing power by reason of his possession of company checks and the use of the Sureaz signature stamp, and that certain of the fraudulent income tax returns apparently bore Nanni’s handwriting although he had not signed them as preparer. The Report identified Nanni as a probable participant in a fraudulent conspiracy and named him as one of those of whom investigation was recommended. The evidence recounted in Ricotta’s Report constituted a proper and independent source for pursuit of an investigation against Nanni. Against the background of this evidence developed by Ricotta and cited extensively in DelValle’s initial evaluative summary, the district court could properly credit DelValle’s uncontradicted testimony that he did not use Nanni’s grand jury testimony in deciding to investigate Nanni or to pursue leads. We conclude that the district court properly ruled that those initial decisions did not violate Nanni’s Fifth Amendment rights.
a. The Application for an Undercover Operation
DelValle’s November 1989 application to the CID managers for permission to conduct an undercover operation targeted Latin, Zueco, Laraby, Nanni, and “JOHN SUREAZ— Owner of record, believed to be a fictitious person.” The application continued:
It is alleged that the proposed targets conspired to divert substantial amounts of retained earnings from AJS Merchandising, Inc., failed to report as much as one third of the annual gross receipts of the corporation and concealed the diversion of funds from the Internal Revenue Service by creating a fictitious person, John Sureaz, as the President and sole-stockholder of AJS Merchandising, Inc.
After describing the earlier state-court obscenity investigation, the application stated that
[djuring the course of the investigation, the Niagara County District Attorney’s Office attempted to verify the existence of John Sureaz and was unable to do so.
In 1987, the Examination Division began an audit of AJS Merchandising, Inc. for the years 1983 through 1986. During the course of the audit, Latin stated to an Internal Revenue Service Agent that he did not meet John Sureaz until immediately prior to the sale of the business to him. Since the sale, no one associated with Good Time Charlie’s [sic ] has been able to provide an accurate description of Sureaz or any means of contacting him.
The application proceeded to describe each of the proposed targets. With respect to Sureaz and Nanni, it stated as follows:
JOHN SUREAZ
He is shown on the New York State Certificate of Incorporation and the Federal tax returns for AJS Merchandising, Inc. as the sole shareholder and president. Evidence obtained in the investigation indicates that John Sureaz is a fictitious person. It is alleged that the sale of Good Time Charlie’s [sic ] was a sham instituted to create a fictitious person as the owner, thereby insulating the true owner(s) irom prosecution for obscenity violations. In addition, it has also allowed the true owners) to further a scheme of diverting prof*1439its from the business and evading his individual income taxes.
It is believed that the only original signature containing the name John Sureaz is the Certificate of Incorporation. All other known documents, including the signature card and cancelled checks for the corporate bank accounts and tax returns contain a stamped signature. The corporate accountant, Carl Nanni, is known to use the “John Sureaz” signature stamp.
CARL NANNI
He resides at 682 Van Voorhees Avenue, Rochester, New York. He was the accountant for DiHar, Inc. and is also the accountant for AJS Merchandising, Inc. Nanni prepared all of the returns for the two corporations as well as Latin’s individual returns up to 1986. Nanni is known to have been the accountant for organized crime figures in the Rochester area and was previously the subject of an IRS criminal investigation. Nanni is currently operating his accounting business under his daughter’s name, since the Treasury Card allowing him to practice before the Internal Revenue Service was revoked. The revocation was based on a New York State conviction on embezzlement charges.
The application made no mention of Nanni’s grand jury testimony.
At the Kastigar hearing, DelValle testified as follows with regard to the undercover operation application:
Q. Did you have any role in preparing that document?
A. Yes.
Q. Do you recall — well, do you recall writing in the document during the course of this investigation, the Niagara County District Attorney’s office attempted to verify the existence of John Sureaz and was unable to do so. Do you call writing that statement?
A Yes, I do.
Q. What was the basis for — your basis of knowledge for making that statement?
A My contacts with the district attorney’s office.
Q. That would include your conversation with Mr. Broderick?
A. Yes.
Q. That would include your review of the trial transcripts at — of the Niagara County obscenity—
A. Right.
Q. —case?
A. Yes.
Q. That would include your review of the grand jury material Mr. Broderick made available to you?
A. Yes.
(June 18 Tr. at 63-64 (emphasis added).)
In April 1990, DelValle also applied for an extension of the undercover operation, again identifying Sureaz as “an individual believed by several government agencies to be a fictitious character created to insulate Latin and others from prosecution by the IRS, FBI and other government agencies.” At the Kastigar hearing, DelValle testified as follows:
Q. What was the basis of knowledge when — at the time that you wrote that statement?
A. The IRS and FBI efforts to locate Mr. Sureaz through a nationwide search, the Niagara County — the obscenity trial, their attempts to locate him, and the undercover agents’ inability or the undercover agents’ contacts.
Q. Was part of the basis of your knowledge in making that statement that the Niagara County District Attorney’s office had conducted an investigation to try to verify the existence of John Sureaz and had been unable to do so?
A. That was part of it, yes.
Q. Was part of the basis for your making the statement the answers that Carl Nanni gave to Mr. George Burgasser concerning the location, whereabouts of John Sureaz and the circumstances under which he knew John Sureaz?
A. I’m not — I think I concentrated more on the trial because at the trial there were several individuals brought in to verify Sureaz, not just — I don’t believe I really went through Carl Nanni’s testimony — I know I didn’t — that thoroughly at any time. You know I just kind of skimmed through it.
*1440Q. Are you trying to say you did not—
A. I did see Carl Nanni’s testimony as I read it but my—
Q. This is the testimony before the grand jury ?
A. Yes, but my evaluations were based on the trial and the attempts to, you,know, by the law enforcement people to try to find John Sureaz. In other words I didn’t focus on Carl Nanni.
Q. Are you saying that that statement had absolutely nothing to do whatsoever with the fact that you reviewed Mr. Carl Nanni’s grand jury testimony?
A. It might have been. It wasn’t the sole—
Q. It was a factor, but not the sole factor?
A. Yes, I suppose.
(June 18 Tr. at 73-75 (emphasis added).)
With respect to the statements in the application that Nanni had notarized Sureaz’s signature and that there existed a rubber stamp of Sureaz’s signature, DelValle testified as follows:
Q..... You had information developed during the course of this investigation that Carl Nanni notarized John Sureaz’s signature at least once on legal documents, is that right?
A. Yes.
Q. What was your basis of knowledge for that piece of information?
A. The — I believe it was the referral by Ricotta that Carl Nanni had a stamp and Carl Nanni—
A. —and that there were some documents that Carl Nanni had verified and had notarized John Sureaz’s original signature on a document.
Q..... Did you have any other basis of knowledge that you can remember for the information that Carl Nanni had notarized John Sureaz’s signature?
A. I think the testimony or the referral which Mrs. Ricotta had spoken to Mr. Nanni and he had, you know—
Q. When you say testimony, you mean?
A. Well, Mrs. Ricotta had spoken to Mr. Nanni as a third-party witness.
Q. Okay. You said testimony, that refers to court testimony or grand jury testimony?
A. Not necessarily. If you — if you interview a witness and you get an affidavit from him or you refer to writing, it’s their testimony. It doesn’t — for us it doesn’t have to be in court.
Q. Okay. So you’re — what you’re telling the Court is that your sole basis of knowledge for Carl Nanni’s having notarized John Sureaz’s signature, your sole basis of knowledge was Barbara Ricotta?
A. Yes.
Q. Now, if I can ask you specifically about the fact, did you develop information to the effect that there was a stamp which had John Sureaz’s signature on it. Did you develop information to that effect that there was a stamp with John Sureaz’s signature on it?
A. Did I personally develop it?
Q. No. Did IRS or did the joint investigation to the best of your knowledge develop that information?
A. No. We knew that, or you know, we had Mrs. Ricotta’s referral that there was a stamp. We would have had no way of verifying it.
Q. You knew from Mrs. Ricotta that a stamp with John Sureaz’s signature existed?
A. Yes.
Q. Did you have any other basis far knowing that?
A, The grand jury testimony of Mr. Nanni.
Q. Okay. Now with respect to this stamp with John Sureaz’s signature on it, did you develop at some point information that the person who had custody or control over the stamp in question was in fact Carl Nanni?
A. No, I didn’t — I didn’t know who had custody and control.
Q. Of the stamp?
*1441A. Right.
Q. You never developed that information? You never became aware of such information during this entire investigation?
A. No. We found the stamp when we did the search warrant at Good Time Charlie’s [sic].
Q. And you’re telling the Court that that was the first time you ever gained any type of information that there might be a connection between this stamp with Sureaz’s signature on it and Carl Nanni?
A. No. I knew Carl Nanni had used a stamp in prior years.
Q. Had used a stamp for what?
A. For, you know, for documents for Mr. Sureaz. He had — I think he had told Mrs. Ricotta that Mr. Sureaz had given him the stamp.
Q. Okay. And was there any other basis for your knowledge that Mr. Nanni had a stamp with Sureaz’s signature on it?
A. Just the grand jury testimony.
Q. Of Carl Nanni?
A. Yes.
(June 18 Tr. at 86-89 (emphasis added).) On redirect examination, DelValle testified that he had seen the stamped signature of Sureaz on AJS’s filed tax returns, that he knew Nanni had notarized AJS’s certificate of incorporation, and that Ricotta’s Report clearly indicated that she had interviewed Nanni and obtained information directly from him in the course of her investigation:
Q. And the document and the information from Miss Ricotta, and which has been introduced into evidence, clearly indicates and stated to you in that report that she had interviewed Carl Nanni?
A. Yes.
Q. And determined from him that he had — he had used a rubber stamp—
A. Yes.
Q. —for John Sureaz, is that correct?
A. Yes.
Q. And that he had — he was the preparer of the tax return—
A. Yes.
Q. —that we just talked about?
A. Yes.
(June 18 Tr. at 95-96.)
As the district court indicated at the hearing, this record indicates that DelValle had Nanni’s grand jury testimony in mind when he applied for authorization to conduct and extend the undercover operation, but that that testimony was not the sole factor, nor even the primary factor. DelValle’s statements that that testimony “might” have had something to do with his application, but that in making his decisions “I didn’t focus on Carl Nanni,” were apparently credited by the court, and we conclude that the record as a whole supports the conclusion that DelValle would have sought the undercover operation entirely apart from Nanni’s grand jury testimony.
As to the CID managers who made the decision whether or not to grant DelValle’s request for initiation and continuation of an undercover operation, the question is even more clear-cut. The application made no mention whatever of the fact that Nanni had testified before the State grand jury, and each material fact that could have been based on that testimony had been turned up independently by Ricotta. We conclude that the CID managers’ decision to authorize the undercover operation could not have been influenced by the immunized testimony.
b. The Handwriting Exemplars
Nor do we have any difficulty in upholding the district court’s ruling with respect to the federal grand jury’s request for Nanni’s handwriting exemplar. At the Kastigar hearing, DelValle testified that it had been decided to “subpoena any individuals who may have had the ability or the opportunity to use the stamp or to prepare the stamp for handwriting exemplars.” (June 18 Tr. at 91.) He elaborated as follows:
Q. And would that include individuals who had access to the stamped signature?
A. Yes, that would have included them.
Q. And you knew that one of the individuals who had access to the stamped signature was Carl Nanni?
*1442A. Yes.
Q. And you knew that at the time of this meeting at which you decided to subpoena Carl Nanni for the exemplars?
A. Yes, I knew that.
Q. Okay. And you testified earlier that the basis for your knowledge as to who had the stamp was your review of Barbara Ricotta’s report and your review of Carl Nanni’s grand jury testimony?
A. Yes.
(June 18 Tr. at 92-93.)
The district court properly concluded that the government established that it would have sought handwriting exemplars without regard to Nanni’s grand jury testimony. DelValle’s testimony, as recounted in this and the preceding section, indicated that the primary impetus for seeking a sample for Nanni’s handwriting was Ricotta’s Referral Report. The need for handwriting exemplars was plainly indicated in the Report, which stated, for example, that one of the fraudulent tax returns appeared to be in Nanni’s handwriting though he was not listed thereon as preparer, and that the Sureaz signature on one return appeared to have been forged and may have been written by Nanni. Further, there is no evidence that DelValle mentioned Nanni’s immunized State grand jury testimony to the federal grand jury in connection with the latter body’s decision whether to request handwriting exemplars. Thus, the district court properly concluded that Nanni’s grand jury testimony had not been used in obtaining the handwriting exemplars.
c. The Search Warrant Application
DelValle’s affidavit in support of the government’s application for search warrants presents the most troublesome issues, for that affidavit cited and described Nanni’s grand jury testimony. After stating that there was reason to believe that Latin, Nanni, Laraby, and others had conspired to defraud the government of taxes, in part by means of “creat[ing] a fictitious owner and president of AJS Merchandising, Inc., i.e. John Sureaz” (emphasis in original), the DelValle affidavit continued, in pertinent part, as follows:
19. The only known existence of Sureaz has been testimony by Carl Nanni that he, in fact, knew Sureaz and he (Nanni) notarized Sureaz’s signature on the incorporation papers of AJS Merchandising, Inc. The following investigative steps have been taken to verify the existence of John Sureaz, the alleged president of AJS Merchandising, Inc.:
A) a nationwide search of the Department of Motor Vehicles showed no record of a John Sureaz ever having a driver’s license or owning or registering an automobile;
B) Social Security records have no social security number or any social security records whatsoever on an individual named John Sureaz;
C) an Internal Revenue Service check was performed nationwide to determine if an individual named John Sureaz had filed income tax returns during the last seven years. This search also proved negative. There was no record of a John Sureaz ever filing an income tax return.
20. The investigation, to date, has also disclosed the following inconsistencies relative to the existence of John Sureaz:
A) Carl Nanni, testified before a'Niagara County Grand Jury relative to Good Time Charlie’s [sic] in July 1988 and January 198b The grand jury testimony has been provided to your Affiant by the Office of the Niagara County District Attorney. Nanni testified that he notarized John Sureaz’s signature on the incorporation papers for AJS. Nanni further testified that he met John Sureaz “sometime last year” and that Saverio Latin had introduced Sureaz to him (Nanni). Nanni further testified that he had ended up doing AJS Merchandising’s accounting because Latin had introduced Sureaz to him and Sureaz had indicated that he needed someone to do the accounting work for AJS.
B) However, on June 4, 1990 during a meeting between Nanni and an undercover agent of the Internal Revenue Service, Nanni stated that [he] (Nanni) *1443introduced Sureaz to Saverio Latin and that he (Nanni) had known Sureaz for years and that Sureaz was, at the present time, residing in the Rochester area. Nanni further stated that he would make an attempt to get in touch with Sureaz and make him available to the undercover agent.
C) On March 2, 1990, during a meeting between an undercover agent and Saverio T. Latin, Latin stated that John Sureaz resides in Boston, Massachusetts.
D) On March 28, 1990 during a meeting between an undercover agent and Robert Zueco, the attorney for AJS, ARS and Saverio T. Latin, Zueco stated that John Sureaz resides somewhere in Southern California, probably around the San Diego area.
Carl Nanni also testified before the Niagara County Grand Jury and confirmed in a meeting on June 13, 1990 with an undercover agent that he regularly used a rubber stamp containing the signature of John Sureaz.
21. Another investigative approach utilized by the Internal Revenue Service in its investigation of the foregoing scheme included the use of undercover agents who have personally met with Saverio T. Latin, Brian Laraby, Robert Zueco and Carl Nanni in an attempt to purchase Good Time Charlie’s [sic ] and the real property on which it is located.
(Emphasis added.)
Plainly, DelValle’s affidavit, submitted in support of the government’s application for the search warrants that eventually resulted in the seizure of the Sureaz signature stamp, along with some of the documents the government intended- to use at trial, actually used Nanni’s immunized grand jury testimony. This use, insofar as the prosecution of Nanni is concerned, violated Nanni’s Fifth Amendment rights. The question thus becomes whether that use was harmless beyond a reasonable doubt in the sense that the immunized testimony was so inconsequential that it could not have influenced either the government’s decision to request search warrants or the issuing magistrate’s decision to grant them.
We conclude that the district court'properly found the violation harmless, for there can be no reasonable doubt that even absent Nanni’s grand jury testimony, the government would have applied for search warrants, and that, had the affidavit omitted these references, the magistrate would have, properly, issued the warrants. The tainted portion of the DelValle affidavit, appearing only in paragraphs 19 and 20, was but a small fragment of that 31-page affidavit. Indeed, most of paragraphs 19 and 20 themselves recounted independently gained information strongly indicating that Sureaz was a fiction. The bulk of the remainder of the affidavit summarized in detail the evidence of tax evasion supplied by confidential informants and by the targets themselves in taped conversations with undercover agents. For example, it summarized evidence provided by one confidential informant, who had worked at Good Time Charlies between 1986 and 1987, that he and other employees had received half their pay “off the books” and that receipts from the sale of tokens for peep shows, amounting to roughly one-third of gross income, was recorded separately from other income. The informant, who had never heard of John Sureaz, also reported that Latin exercised complete control of Good Time Charlies despite the purported sale of the business to AJS, and that the informant had been approached once with a proposition to put ownership of Good Time Charlies in his name.
DelValle’s summary and quotation in his affidavit of recorded conversations between undercover agents and individuals involved with Good Time Charlies strongly established probable cause for the issuance of the requested search warrants. For example, it was plain that the building owned by Latin and the Good Time Charlies business purportedly sold by Latin to Sureaz in 1982 went hand-in-hand. When agents representing to Latin that they were prospective buyers of the building asked whether the $1.5 million asking price was for the building alone, they were told, “‘hey, you’re not spending a million and a half for the property cause it ain’t worth a million and a half for *1444the property. You’re spending a million and a half for the business.’ ”
As to Latin’s claims with respect to the value of the business itself, DelValle’s affidavit described Latin’s statements to the undercover agents that Good Time Charlies had weekly income of $10,000, which had been as high as $13,000, and Latin’s showing the agents daily income sheets reflecting true receipts of the business. The DelValle affidavit provided weekly income figures taken from AJS’s tax returns which showed roughly half the amounts Latin represented to the undercover agents. Further, Latin told the agents “‘there’s always two sets of numbers.’ ” Latin said he used the first set to make his own records and then destroyed that set; he sent the second set to his accountant for the preparation of the tax returns. Nanni too told the undercover agents that AJS’s tax returns reported incorrect figures and that both Nanni’s office and Latin had records which demonstrated that the true receipts were much higher — between $12,000 and $13,000 a week.
DelValle’s affidavit also pointed out inconsistencies in the suspects’ statements to the undercover agents as to where Sureaz lived. Latin said Boston; Nanni said Rochester; Zueco said San Diego. DelValle’s affidavit informed the court that nationwide searches the Social Security Administration, the IRS, and the records of the departments of motor vehicles nationwide, had revealed no evidence of any individual named John Sureaz.
Although DelValle’s affidavit also referred to the immunized grand jury testimony, plainly his original suspicion that Sureaz did not exist was not derived from that testimony. DelValle’s starting point in the matter had been his reading of Ricotta’s Report, which, based on her investigations provided an ample independent basis for the inference that Sureaz did not exist. The evidence recounted in the Report included the facts that Zueco could not give the State sales tax investigator information as to Sureaz’s Social Security Number or whereabouts; that Nanni prepared tax returns for Sureaz though he had virtually no personal contact with him and never put a Social Security Number for Sureaz on any of those returns; that Laraby, who ran GTC’s daily operations, had never had contact with Sureaz; that a confidential informant who worked at GTC for nearly two years had never heard of Sureaz; that Sureaz’s signature was generally affixed by rubber stamp; that in 1982 Latin, who had just met Sureaz, purported to sell Latin’s thriving business to him and lease property to him without knowing his address; and that no one was able to get in touch with Sureaz. The original suspicion created by the Ricotta Report was amply confirmed by the absence of any federal tax filings, social security record, or motor vehicle records anywhere in the United States indicating that an individual by that name existed.
In light of the affidavit as a whole, and the facts that (1) the criminal investigation itself, and (2) the suspicions (a) that Sureaz did not exist, (b) that Nanni had notarized the signature of the nonexistent Sureaz, and (c) that large amounts of income were unreported, did not have their origins in Nanni’s immunized grand jury testimony, we conclude that the district court properly found that the reference to that testimony in the search warrant affidavit, constituting a violation of Nanni’s Fifth Amendment rights, was harmless beyond a reasonable doubt. There can be no reasonable doubt that even absent that testimony the government would have applied for search warrants, probable cause existed for the issuance of the warrants, and the magistrate would have issued them.
CONCLUSION
We have considered all of Nanni’s arguments on this appeal and have found in them no basis for reversal.- The judgment of conviction is affirmed.