CORRECTED SUMMARY ORDER
Defendant-appellant Philip A. Giordano appeals from a June 13, 2003 judgment of conviction and sentence entered after a jury trial before the United States District Court for the District of Connecticut (Nev-as, J.). Giordano, formerly the mayor of Waterbury, Connecticut, was convicted of two counts of civil rights violations under color of law in violation of 18 U.S.C. § 242, one count of conspiracy to use a facility of interstate commerce for the purpose of enticing a person under the age of sixteen years to engage in sexual activity in violation of 18 U.S.C. §§ 371 and 2425, and fourteen substantive counts of such use of a facility of interstate commerce in violation of § 2425. The district court sentenced Giordano principally to 444 months’ imprisonment on each of the two § 242 counts; 60 months on the conspiracy count; and 60 months on each of the fourteen § 2425 counts, all to be served concurrently, for a total of 444 months of imprisonment. We address three of Giordano’s challenges to his conviction in a separate published opinion also filed today. In this summary order we discuss his remaining challenges, all of which lack merit. For purposes of this order, we assume the parties’ familiarity with the facts and procedural background of this case.
1) Suppression of wire intercepts and confession
Giordano raises a number of challenges to the district court’s denial of his motion to suppress the intercepted phone calls that formed the basis of his prosecution under 18 U.S.C. §§ 371 and 2425 and led *342to his indictment for violation of 18 U.S.C. § 242. See United States v. Giordano, 259 F.Supp.2d 146, 152-56 (D.Conn.2008). “We review ‘[t]he factual findings on which the district court’s suppression ruling was based ... for clear error, viewing the evidence in the light most favorable to the government; the legal conclusions on which this ruling was based are reviewed de novo. ’ ” United States v. Watson, 404 F.3d 163, 166 (2d Cir.2005) (quoting United States v. Lewis, 386 F.3d 475, 480 (2d Cir.2004)). In re Grand Jury Subpoena Served On John Doe, 889 F.2d 384 (2d Cir.1989), forecloses Giordano’s contention that the court could not lawfully amend a wiretap authorization under 18 U.S.C. § 2517(5) to allow the use of evidence of crimes1 not specified at 18 U.S.C. § 2516. As long as the original order was sought in good faith and not as a “subterfuge search,” § 2517(5) permits use in a subsequent prosecution of evidence of federal crimes that could not have formed the basis for an order ab initio under § 2516.2 Id. at 387-88. We have also carefully reviewed the transcripts of the intercepted calls and find that, while Giordano is correct that certain phone calls placed before July 2001 include brief references to the youth of the victims, the district court did not clearly err in concluding that the government was not aware of their significance until July, at which point it acted with dispatch to seek amendment under § 2517(5). See Giordano, 259 F.Supp.2d at 154. We affirm the district court’s conclusion that the government acted in good faith and “as soon as practicable” under § 2517(5) for the reasons given by the district court. Id.
We reject Giordano’s argument that the government did not adhere to the minimization requirements of 18 U.S.C. § 2518(5) for the reasons stated by the district court. Id. at 154-55 (citing United States v. Capra, 501 F.2d 267, 275-76 (2d Cir.1974)).
We also reject Giordano’s argument that the district court erred in denying his motion for a Franks hearing. As the district court found, Giordano’s affidavit was insufficient to establish that the agent who procured the warrant did so knowing of or with reckless regard to the falsity of the agent’s affidavit. See Velardi v. Walsh, 40 F.3d 569, 573 (2d Cir.1994) (“Unsupported eonclusory allegations of falsehood or material omission cannot support a Franks challenge; to mandate a hearing, the plaintiff must make specific allegations accompanied by an offer of proof.”).
Finally, Giordano argues that the district court erred in denying his motion to suppress statements he made to federal agents between July 23 and July 25, 2001 because of the government’s asserted violation of Federal Rule of Criminal Procedure 5(a) and the rule of United States v. Perez, 733 F.2d 1026 (2d Cir.1984). The predicate of this argument is that Giordano was “taken into custody” at 12:15 PM on July 23. Remarkably, Giordano makes no mention whatsoever of the district court’s conclusions following a thorough *343hearing that Giordano was not under arrest until July 26 and that, even if it is supposed that Giordano had been in custody during the relevant period, the statements in question were made voluntarily. See Giordano, 259 F.Supp.2d at 156-60. We deem any challenge to these findings abandoned, and decline to consider this argument. See, e.g., Briarpatch Ltd., L.P v. Phoenix Pictures, Inc., 373 F.3d 296, 301 (2d Cir.2004). We note, in any event, that we perceive no error in the district court’s analysis, see 259 F.Supp.2d at 156-60, and that even assuming arguendo that suppression of the statements were required under Perez, the government was not barred from using them to impeach Giordano’s trial testimony. See Harris v. New York, 401 U.S. 222, 225-26, 91 S.Ct. 643, 28 L.Ed.2d 1 (1971).
2) Interviews with child witnesses and remote testimony
Giordano challenges the district court’s ruling permitting the child victims to testify remotely under 18 U.S.C. § 3509. He argues that the requisite showing under § 3509(b)(l)(B)(i) that “[t]he child is unable to testify [in person] because of fear” of the defendant cannot be made, as it was in the case of VI,3 through non-expert testimony. Giordano’s reliance on United States v. Moses, 137 F.3d 894 (6th Cir.1998) is misplaced. Its holding regarding the expert testimony requirement concerns § 3509(b)(l)(B)(ii), which, unlike section 3509(b)(l)(B)(i), requires the use of expert testimony. See id. at 899. Contrary to Giordano’s assertion, Maryland v. Craig, 497 U.S. 836, 110 S.Ct. 3157, 111 L.Ed.2d 666 (1990), does not require that a decision to allow a child witness to testify remotely be based on expert testimony. See id. at 860, 110 S.Ct. 3157 (“[W]e decline to establish, as a matter of federal constitutional law, any ... categorical evidentiary prerequisites for the use of the one-way television procedure.”). The district court’s factual findings as to both victims satisfy the requirements of Craig, see id. at 855-58, 110 S.Ct. 3157 and are not clearly in error.4
3) Evidentiary rulings
Giordano raises numerous challenges to evidentiary rulings of the district court at trial. None of the challenged rulings represent an abuse of discretion.5 See United States v. Lewter, 402 F.3d 319, 323 (2d Cir.2005). The district court was within its discretion under Federal Rule of Evidence 608(b) to permit questions concerning the nature of the corrupt activities that led to Giordano’s receipt of cash payments. See, e.g., United States v. Bustamante, 45 F.3d 933, 946 (5th Cir.1995) (holding that solicitation of bribes is relevant to the issue of truthfulness under R. 608(b)). *344Giordano’s own testimony opened the door to each of the remaining challenged lines of questioning. See United States v. Beverly, 5 F.3d 633, 639 (2d Cir.1993) (“Once a defendant has put certain activity in issue by offering innocent explanations for or denying wrongdoing, the government is entitled to rebut by showing that the defendant has lied.”).
The district court also did not abuse its discretion under Federal Rules of Evidence 402, 403 and 412(b)(1)(C) in prohibiting cross-examination of the victims regarding past sexual activity. See United States v. Purdy, 144 F.3d 241, 246 (2d Cir.1998) (“[JJudges are accorded wide latitude in excluding evidence that poses an undue risk of harassment, prejudice [or] confusion of the issues or evidence that is ... only marginally relevant.” (internal quotation marks omitted; second alteration in original)). Contrary to Giordano’s assertion, the source of the children’s knowledge of sexual terms was not at issue in the trial.
4) Sentencing
Giordano raises a host of challenges to the computation of his sentence under the Sentencing Guidelines. “We review the district court’s interpretation and application of the Guidelines de novo and its factual determinations underlying the application of the Guidelines for clear error.” United States v. Szur, 289 F.3d 200, 215 (2d Cir.2002). The government concedes that the district court impermissibly double-counted in imposing a two-level enhancement for “serious bodily injury” under U.S.S.G. 2A3.1(b)(4)(B),6 because that term is defined in Application Note 1 to U.S.S.G. 2A3.1 to exclude criminal sexual abuse and the record did not show that the victims suffered other serious bodily injury. Without this enhancement, the adjusted offense levels for Counts One and Two of the indictment are 41, instead of 43. As explained below, however, this error is harmless, because the combined offense level under U.S.S.G. 3D1.4 remains 43, the maximum possible adjusted level, even if the adjusted offense level for Counts One and Two is reduced.
Contrary to Giordano’s assertion, the enhancement to the § 2425 counts under U.S.S.G. 3B1.3 for abuse of public trust and the offense characteristic enhancement applied to the § 242 offenses under U.S.S.G. 2Hl.l(b) for acting while a public official do not represent impermissible double-counting. “[D]ouble counting is permissible in calculating a Guidelines sentence where, as here, each of the multiple Guidelines sections applicable to a single act serves a distinct purpose or represents a discrete harm.” United States v. Maloney, 406 F.3d 149, 153 (2d Cir.2005). The 3B1.3 enhancement reflects the increased culpability of persons who take undue advantage of a position of trust and discretion (which may be public or private) to commit crimes with a greater chance of impunity. See U.S.S.G. § 3B1.3 app. n.l & background. As applied to Giordano’s § 2425 offense, the goal of this enhancement is to punish abuse of his mayoral position to commit sexual abuse. The 2Hl.l(b) offense characteristic vindicates a distinct interest, namely the “compelling public interest in deterring and adequately punishing those who violate civil rights under color of law,” and does not preclude separate enhancements intending to capture “a victim’s increased vulnerability to [the] defendant’s illegal conduct.” United States v. Hershkowitz, 968 F.2d 1503, 1505 (2d Cir.1992) (so holding with respect to predecessor adjustment under U.S.S.G. *3452H1.4 for offenses committed under actual or purported legal authority); see also United States v. Volpe, 224 F.3d 72, 76-77 (2d Cir.2000) (same as to present U.S.S.G. 2Hl.l(b) and enhancement for vulnerable victim under U.S.S.G. 3A1.1).
Giordano also argues that the district court’s grouping analysis was infected with error. While that analysis was not a model of clarity, we conclude that any error was harmless. The district court adopted the analysis of the presentence report (“PSR”), which correctly noted that both U.S.S.G. 2H1.1 (controlling the § 242 counts) and 2G1.1 (controlling the § 2425 counts) are specifically excluded from operation of the grouping mechanism under U.S.S.G. 3D1.2(d). The PSR then concluded that the offenses are “not grouped,” apparently without reaching any conclusion as to the propriety of grouping under any other subsection.7 See U.S.S.G. 3D1.2(d) (providing that “[e]xclusion of an offense from grouping under this subsection does not necessarily preclude grouping under another subsection” of 3D1.2). We do not need to resolve whether grouping was required under 3D1.2(a), (b) or (c) with respect to each victim in this case, because, as the district court itself found, the grouping of offenses could result in no mathematical difference to the combined offense level and resulting Guidelines range in light of the Guidelines’ overall cap at 43, U.S.S.G. 5 Pt. A app. n.2. The correct adjusted offense level for each of the § 242 counts was 41, as the highest offense level, 41 would serve as the base of the district court’s combined offense level calculation. U.S.S.G. 3D1.4. The adjusted offense level for each § 2425 offense was 39, meaning that each such offense or group of offenses would yield one additional unit under 3D1.4(a). Giordano concedes, as he must, that offenses relating to VI and V2 cannot be grouped with each other,8 so the district court would have been constrained to add two levels to the base of 41 even if all counts relating to each victim were grouped, yielding the same combined offense level of 43. See U.S.S.G. § 3D1.4(a).
We do not consider Giordano’s challenge to the district court’s decision not to depart downwardly on grounds other than U.S.S.G. 5K1.1 because the district court did not misapprehend the scope of its departure authority. See Volpe, 224 F.3d at 78.
5) Recusal
Finally, we reject Giordano’s argument that Judge Nevas should have recused himself from presiding at trial on the basis of remarks made at a bail hearing. Judge Nevas did not abuse his discretion in denying this recusal motion. See King v. First American Investigations, Inc., 287 F.3d 91, 96 (2d Cir.2002); United States v. Arena, 180 F.3d 380, 398 (2d Cir.1999).
We have considered Giordano’s remaining arguments and conclude that they are without merit.
For the foregoing reasons and those set forth in the accompanying published opinion, we AFFIRM the judgment of convic*346tion and sentence to the extent appealed from, without prejudice to Giordano’s ability to seek a remand pursuant to United States v. Fagans, 406 F.3d 138 (2d Cir. 2005) or United States v. Crosby, 397 F.3d 103 (2d Cir.2005), as appropriate. Giordano is hereby ORDERED to inform the Court by letter-brief not to exceed three pages, within fourteen days of receipt of this Order, whether he seeks such a remand and, if so, whether his challenge to the constitutionality of the application of the Guidelines to his sentence was preserved below, and to append thereto any relevant portions of the record. The government may, but need not, respond to that submission, by letter-brief not to exceed three pages, within seven days of receipt of Giordano’s letter.
. We reject Giordano's contention that the intrastate phone calls between Giordano and Jones did not constitute criminal acts under 18 U.S.C. § 2425 for the reasons set forth in the published opinion that accompanies this Order, See United. States v. Giordano, 442 F.3d 30, 39-44 (2d Cir.2006).
. To the extent Giordano's invitation to overrule In re John Doe, 889 F.2d at 384, is based on his argument that the Fourth Amendment forbids its construction of § 2517(5), we note that even if we were free to revisit the holding of In re John Doe, we would not disturb it. As the district court held, § 2517(5) is a statutory expression of the plain view doctrine, which allows the use of evidence fortuitously discovered in the course of an authorized search. See Giordano, 259 F.Supp.2d at 154-55 (citing United States v. Masciarelli, 558 F.2d 1064, 1067 (2d Cir.1977)).
. As in the published opinion, we refer to the child victims, whose names remain under seal, as “VI” and "V2.” See United States v. Giordano, 442 F.3d 30, 34 (2d Cir.2006).
. Giordano also argues that his Sixth Amendment right to confront witnesses and his Fifth Amendment right to a fair trial were violated when the district court rejected his motion to allow defense counsel or an “independent monitor” to attend interviews of the child victims by the government's attorney prior to trial, or in the alternative, to disallow the interview. The only authority Giordano cites for this novel assertion is Craig. Neither Craig nor any other case of which we are aware offers support for Giordano’s position. We note that Giordano was permitted to and did elicit from the child victims on cross-examination the fact that they had previously met with the government’s attorney and were familiar with the questions they would be asked at trial.
. We review Giordano’s challenge to the prosecutor’s questions concerning his violation of assorted oaths for plain error because he made no objection at trial, see United States v. Li, 115 F.3d 125, 129 (2d Cir.1997), and find none.
. This and all subsequent citations refer to the United States Sentencing Commission Guidelines Manual effective November 1, 2002.
. The PSR proceeded to analyze, in addition to the two § 242 counts, only five representative additional counts, based on the mistaken premise that the combined offense level would be unaffected by the adjusted offense level of further offenses because they would not result in the addition of additional units to the combined offense level. This was error, as the government concedes, because there must be "more than 5” units added for additional offenses under 3D. 14 before incremental units fail to increase the combined offense level. For reasons explained infra, this error makes no difference to the proper Guidelines range.
. For the § 2425 offenses in which both girls were named, the Guidelines specifically instruct that each such count should be treated as two separate counts for grouping purposes. U.S.S.G. 2Gl.l(d).