VAN GRAAFEILAND, Senior Circuit Judge:

Gregory Boutte appeals from a judgment convicting him on five counts of wire fraud ( 18 U.S.C. § 1343), five counts of submitting false claims to a federal agency ( 18 U.S.C. § 287) and thirteen counts of making false statements to a federal agency ( 18 U.S.C. § 1001). Boutte contends that the district court committed reversible error in denying certain pretrial motions, making an improper evidentiary ruling and giving defective instructions to the jury. He also argues that the district court erroneously calculated his sentence. Finding no merit in these contentions, we affirm.

During government fiscal years 1988 through 1991, Boutte and his accounting partnership, Boutte, Elmore Company, operated the Triplex Minority Business Development Center. Triplex was one of a number of development centers funded by the United States Department of Commerce for the purpose of promoting the growth of minority-owned businesses. The Department of Commerce awarded Triplex funding of $165,000 for each fiscal year. To establish that Triplex continued to meet the goals of the program, Boutte and the partnership were required to submit quarterly narrative reports ("QNRs") to the Department. The QNRs summarized the level of contract opportunities or financing that minority businesses had received with the assistance of Triplex. They also identified the partnership personnel assigned to Triplex and the percentage of time these employees devoted to Triplex matters. Triplex's failure to report a sufficient amount of services provided to minority businesses could jeopardize the continued federal funding of the center.

The Triplex QNRs from 1988 through 1991 stated that Triplex rendered assistance on numerous occasions to W.B. Construction, J. Allen Contractors and Family Construction. Indeed, these businesses were the purported recipients of most of the assistance Triplex reported during this period. The majority of the QNRs also identified the partnership personnel assigned to Triplex and indicated the percentage of each person's time allegedly devoted to Triplex matters, the percentages varying from 35 percent to 100 percent.

Employees of W.B. Construction, J. Allen Contractors, Family Construction and other businesses testified that they never received the bulk of the assistance reported in Triplex's QNRs. Moreover, Boutte and other partnership employees solicited and received from some of these businesses copies of construction contracts that were entered into without the help of Triplex. Boutte also obtained information about contracts and financing from records the partnership maintained as regular accountant for certain businesses, and Boutte fraudulently added these contracts and financing to the QNRs to bolster Triplex's assistance statistics. In addition, both clients and employees of Boutte, Elmore Co. testified that individuals assigned to work for Triplex devoted significantly less of their time to Triplex matters than was reported in the QNRs. Boutte attempted to disguise these discrepancies by creating two different sets of timesheets — one for Triplex and one for the partnership.

After being fired, Agustus Bodah, a partnership employee who was reported to have devoted 100 percent of his time to Triplex, contacted Commerce officials to report the occurrence of fraudulent activities. Federal agents then obtained a search warrant for the Triplex offices and a storage warehouse, and seized voluminous documents at both locations. On October 17, 1991, a 23-count indictment was returned against Boutte, the partnership and several employees. Boutte moved before trial for production of the search warrant affidavit, for leave to file a suppression motion within a reasonable time after receiving the affidavit, and for a bill of particulars. The Government opposed these motions and requested that the search warrant affidavit be reviewed in camera because it disclosed the identity of a confidential informant.

The district judge denied all three motions. With regard to the warrant affidavit, he said that he had reviewed it in camera and found it more than sufficient to support the issuance of the warrant. Defense counsel was given a copy of the affidavit during the trial. However, it was not made part of the record, and we have no knowledge of its contents except that we are given to understand that the confidential informant was Bodah.

We must express some wonderment as to why the district court deemed it necessary to protect the identity of the informant Bodah and why the warrant affidavit could not have been redacted sufficiently to remove Bodah's name. Having said this, we hasten to add that Boutte has not disclosed any prejudice requiring reversal. Boutte has had a copy of the warrant affidavit in his possession since June 29, 1992, and he has not deemed it necessary to get it before this Court. We assume that, if the affidavit was inadequate or if any of its contents were prejudicial, Boutte would have made certain that a copy of the affidavit was in our hands. We disagree with Boutte's argument that simply "by thwarting the application of the Federal Rules of Criminal Procedure, the trial court deprived the appellant of due process of law under U.S. CONST. amend. V." (Appellant's Brief 13) The Rules of Criminal Procedure per se are not the equivalent of constitutional dogma. Boutte must show with some specificity why the district court's ruling hampered him in his defense. See United States v. Diaz, 655 F.2d 580, 585-89 (5th Cir. 1981); United States v. Hare, 589 F.2d 242, 243 (5th Cir. 1979); see also United States v. Mueller, 902 F.2d 336, 341 (5th Cir. 1990).

Boutte's argument that the district court's rulings deprived him of his Sixth Amendment right to the benefit of counsel contains no citation of supporting authority, and, of course, there is none.

The district court did not abuse its discretion in denying Boutte's motion for a bill of particulars. Boutte requested the identification of an individual whose working hours were at issue in counts 1-5, and who was described only as a Triplex "business specialist." Boutte also sought identification of the "various clients" who, according to counts 11-23 of the indictment, did not receive the services reported in Triplex's QNRs. The information Boutte sought was available to him in the QNRs he submitted to the Department of Commerce, and he failed to establish that the district court's ruling resulted in "`actual surprise at trial and . . . prejudice to his substantial rights.'" United States v. Moody, 923 F.2d 341, 351 (5th Cir.) (quoting United States v. Marrero, 904 F.2d 251, 258 (5th Cir.), cert. denied, 498 U.S. 1000, 111 S.Ct. 561, 112 L.Ed.2d 567 (1990)), cert. denied, ___ U.S. ___, 112 S.Ct. 80, 116 L.Ed.2d 54 (1991); see United States v. Diecidue, 603 F.2d 535, 563 (5th Cir. 1979), cert. denied, 445 U.S. 946, 100 S.Ct. 1345, 63 L.Ed.2d 781 (1980).

Boutte also contends that the district judge erred in instructing the jury on the concept of deliberate ignorance. Although Boutte does not challenge the correctness of the instruction as an abstract statement of the law, he asserts that the evidence below did not support the instruction because it created no inference that he purposely contrived to avoid becoming aware that the QNRs contained incorrect and deceptive statements.

A deliberate ignorance instruction must not be simply an abstract statement of the law; it must state the legal principles as they might be applied to the facts of the case being tried. United States v. Cartwright, 6 F.3d 294, 300 (5th Cir. 1993). There is nothing to indicate that Boutte consciously avoided becoming aware of the fraudulent activities related to Triplex. Rather, the evidence shows that Boutte took steps to become actively involved in the illegal conduct. For example, he personally solicited copies of contracts from certain construction firms for deceptive inclusion in the QNRs; he personally assigned Triplex personnel to perform work for the partnership that was charged to Triplex; he instructed Triplex personnel to prepare two sets of time sheets in order to disguise their partnership work, and he personally reviewed these dual time sheets. His claim that he did not believe his acts were wrongful does not demonstrate that he took steps to avoid learning of the illegal conduct at the time of its commission. See United States v. Lara-Velasquez, 919 F.2d 946, 951 (5th Cir. 1990).

To the extent that the district court's charge was error, however, the error was harmless. In Cartwright, supra, this Court held that, where there is no evidence of conscious ignorance, a deliberate ignorance instruction "is `surplusage' and thus does `not create the risk of prejudice.'" 6 F.3d at 301 (quoting United States v. Samuel, 980 F.2d 1443 (5th Cir. 1992) (unpublished), cert. denied, ___ U.S. ___, 113 S.Ct. 2967, 125 L.Ed.2d 667 (1993)). Giving an instruction on deliberate ignorance also constitutes harmless error where substantial evidence of actual knowledge exists. See id.; United States v. Rivera, 944 F.2d 1563, 1572-73 (11th Cir. 1991).

We find no merit in Boutte's contention that with respect to the misrepresentations alleged in counts 6-10 of the indictment, the district court's charge omitted the allegations in the indictment specific to his case. Although the district judge did not recite the specific language of the indictment with respect to counts 6-10, he did not permit the jury to convict Boutte "upon a factual basis that effectively modifies an essential element of the offense charged." United States v. Doucet, 994 F.2d 169, 172 (5th Cir. 1993). The district judge properly set forth the elements of the offense described in 18 U.S.C. § 287 and correctly paraphrased the language of that section. He predicated conviction upon a factual basis that satisfied the essential elements of section 287. Moreover, there was little or no variance between the allegations of counts 6-10 and the evidence introduced at trial. Thus, no uncertainty exists as to whether the jury convicted Boutte for an offense not charged in the indictment. See United States v. Young, 730 F.2d 221, 223-24 (5th Cir. 1984).

We also reject Boutte's contention that the district court erred in failing to instruct the jury adequately on unanimity with respect to counts 6-10 and counts 11-23. With respect to counts 6-10, the district judge instructed the jury solely with respect to the filing of improper claims, not QNRs:

For you to find any defendant guilty of this crime you must be convinced that the government has proved each of the following beyond a reasonable doubt. First, that such defendant knowingly presented to an agency of the United States a false or fraudulent claim against the United States, and second, that such defendant knew that the claim was false or fraudulent.

These claims, entitled "Request for Funds," were admitted into evidence as exhibits 64-68; they are the specific claims set forth and identified in the indictment. Boutte is wrong, clearly wrong, in his contention that under the court's charge the jury could have convicted him on counts 6-10 of either making false claims for payment or filing false QNRs. Moreover, the fact that the jury might have based its finding of guilt upon either the falsity or fraudulence of the filed claims did not vitiate the verdict. See Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 654, 24 L.Ed.2d 610 (1970); Smith v. United States, 234 F.2d 385, 389 (5th Cir. 1956); Heflin v. United States, 223 F.2d 371, 373-74 (5th Cir. 1955); with specific reference to 18 U.S.C. § 287 see United States v. Murph, 707 F.2d 895, 896-97 (6th Cir.), cert. denied, 464 U.S. 844, 104 S.Ct. 145, 78 L.Ed.2d 136 (1983); United States v. Maher, 582 F.2d 842, 846-47 (4th Cir. 1978), cert. denied, 439 U.S. 1115, 99 S.Ct. 1019, 59 L.Ed.2d 73 (1979).

Boutte's further contention that, although the judge's charge "included some general language requiring unanimity," it "did not require the jury to be unanimous as to which of the two theories for conviction, i.e., either `fraudulent' claims for payment or merely `false' quarterly reports, supported a guilty verdict in Counts 6 through 10" (Appellant's Brief 32) simply repeats appellant's misinterpretation of the court's charge already discussed in the preceding paragraphs.

Counts 11-23, on the other hand, deal clearly with the making of false and fraudulent QNRs, each count referencing a specific, dated report. The district court instructed the jurors that their verdict must be unanimous on each count. No request for a more detailed instruction on unanimity was made, and the suggestions for greater specificity contained in appellant's brief, e.g., the jury must "unanimously agree on the factual basis," are meritless.

Boutte next asserts that the district court erred in allowing the reading in evidence of the letter which Bodah wrote to the Department of Commerce to initiate the Government's investigation of Boutte's activities. The letter was not used to refresh Bodah's recollection. Neither was it offered as a prior consistent statement. Instead, it was offered as a lead-in or guide for Bodah's oral testimony. Its use in this manner was improper. However, Boutte's counsel did not object to this use of the letter, and the error in its use was not so "fundamental as to have resulted in a miscarriage of justice." United States v. Garcia, 995 F.2d 556, 561 (5th Cir. 1993) (per curiam); Ettelson v. Metropolitan Life Ins. Co., 164 F.2d 660, 667 (3d Cir. 1947); Buckley v. United States, 33 F.2d 713, 717 (6th Cir. 1929). Its contents were largely cumulative to the extensive testimony of numerous witnesses, including Bodah himself.

Boutte's final contention is that the district court erred in increasing his Guideline-controlled sentence by four levels for his role in the offense as an organizer or leader. Boutte asserts that the criminal activity for which he was convicted did not involve five or more participants within the meaning of the Guidelines. However, the district court did not clearly err in finding by a preponderance of the evidence that the Guideline requirement was satisfied. See generally United States v. Mergerson, 4 F.3d 337, 347 (5th Cir. 1993). In addition to Boutte himself, see United States v. Barbontin, 907 F.2d 1494, 1498 (5th Cir. 1990), the evidence presented at trial indicated that at least four other employees participated in the fraudulent activities leading to Boutte's conviction. Contrary to Boutte's assertions, these individuals need not have been charged or convicted with him in order to count as participants in the criminal activity; they need only have participated knowingly in some part of the criminal enterprise. See United States v. Alfaro, 919 F.2d 962, 967 (5th Cir. 1990); U.S.S.G. § 3B1.1, comment. (n. 1). Boutte has failed to demonstrate that these Triplex employees did not knowingly play a role in the fraudulent activities and that the district court's finding of participation was clearly erroneous.

The judgment of conviction is AFFIRMED.