A jury found J.D. Todd guilty of three counts of public sexual indecency. The district court sentenced Todd to two and a half years’ imprisonment on each count, to run consecutively. Todd appeals the conviction and sentence.
FACTS
Todd was the teacher-supervisor in charge of discipline at the Lowell Grease-wood Boarding School on the Navajo Reservation in Ganado, Arizona. In May 1987, the FBI began an investigation into allegations that Todd had engaged in sexual misconduct with students at the school. Todd was eventually indicted on twenty-six counts for alleged violations of a variety of state and federal statutes. Before trial, the district court dismissed eight counts charging child molestation, solicitation to commit child molestation, furnishing obscene material to minors, public sexual indecency, and sexual abuse of a minor. Todd was convicted by a jury of the remaining counts, which charged child molestation, public sexual indecency, and sexual conduct with a minor. Five of the counts *927charging sexual conduct with a minor were subsequently dismissed on the government’s motion. The district court then sentenced Todd to a total of ninety-nine years’ imprisonment.
On appeal, we directed entry of a judgment of acquittal on three of the counts of conviction after finding that no rational trier of fact could have found beyond a reasonable doubt that certain offenses occurred on the dates charged. We reversed and remanded as to the remaining ten counts because the district court erroneously admitted the testimony of an expert witness who, in effect, vouched for the credibility of the victim minors who testified.
The government obtained a superseding indictment on nine of the ten remanded counts and added four new counts. The superseding indictment charged Todd with child molestation, sexual conduct with a minor, and public sexual indecency. Prior to and during the second trial, the district court dismissed or directed verdicts on seven counts. The jury found Todd not guilty of three counts, including the remaining charges of child molestation and sexual conduct with a minor, and one count of public sexual indecency. The jury found Todd guilty of three counts of public sexual indecency in violation of Ariz.Rev.Stat.Ann. § 13-1403.1 The district court sentenced Todd to two and one-half years on each of the three counts of conviction, to run consecutively. Todd raises a number of issues on appeal.
Discussion
A. Validity of the Superseding Indictment
Arizona’s public sexual indecency statute proscribes intentionally or knowingly engaging in “sexual contact” or “sexual intercourse” while being reckless as to the presence of a minor under the age of fifteen years. Ariz.Rev.Stat.Ann. § 13-1403.2 “Sexual contact” is “any direct or indirect fondling or manipulating of any part of the genitals, anus or female breast.” Ariz.Rev.Stat.Ann. § 13-1401(2). “Sexual intercourse” is defined as “penetration into the penis, vulva or anus by any part of the body or by any object or manual masturbatory contact with the penis or vulva." Ariz.Rev.Stat.Ann. § 13-1401(3) (emphasis added).
At the time the original indictment was handed down, the government and the grand jury were apparently of the view that masturbation in front of others could constitute “sexual intercourse” within the meaning of sections 1401(3) and 1403(A)(3). The original indictment for each of the three counts of which Todd was eventually convicted accordingly tracked the language of section 1401(3): “J.D. Todd[] intentionally and knowingly engaged in an act of sexual intercourse, to wit: manual masturbatory contact with his penis, and was reckless that [victim’s name], an Indian, a child under the age of fifteen years, was present____”
After Todd’s first trial, but before our decision on his first appeal, the Arizona Court of Appeals made it clear that “sexual intercourse” within the meaning of sections 1401(3) and 1403(A)(3) involves at least two persons. State v. Flores, 160 Ariz. 235, 238-39, 772 P.2d 589, 592-94 (App.1989). Accordingly, after the convictions on these counts were reversed, the government obtained a superseding indictment that made *928the same allegations but removed from the charge only the words “an act of sexual intercourse, to wit: ____”
Because no additional change was made in the charge (such as the substitution of the words “an act of sexual contact, to wit:”), Todd argues that each of the disputed counts in the superseding indictment still charged him with an act of sexual intercourse. He contends that, as a result, he was indicted for one offense, sexual intercourse, and was tried for another, sexual contact. He asserts that he was thus deprived not only of the right to a proper grand jury indictment, but also of notice of the offense for which he was tried. In the alternative, Todd argues that the district court inappropriately allowed the superseding indictment to be constructively amended by permitting the prosecution to prove sexual contact at the second trial rather than sexual intercourse. Todd also argues that the superseding indictment was duplicitous because it joined two distinct crimes—sexual intercourse and sexual contact—in one count, thereby threatening Todd’s right to know the charges against him, right to a unanimous jury, and protection against double jeopardy. See United States v. Aguilar, 756 F.2d 1418, 1420 & n. 2, 1422-23 (9th Cir.1985) (defining and explaining “duplicity”); see also Fed. R.Crim.P. 8(a). We review the validity of the superseding indictment de novo. United States v. Tuohey, 867 F.2d 534, 536 (9th Cir.1989).
In light of Flores, the superseding indictment, which alleged that Todd had manipulated his own penis in the presence of minors, could only have charged the offense of “sexual contact,” which the statute defines to include “any direct ... manipulating of any part of the genitals----” Ariz.Rev.Stat.Ann. § 13-1401(2). See United States v. Mastelotto, 717 F.2d 1238, 1244 (9th Cir.1983) (“if we may fairly read the indictment to charge but one crime in each count, it must be allowed to stand ...”).
Even if the superseding indictment were technically duplicitous, we would not reverse on that ground unless Todd was misled and thereby prejudiced. Aguilar, 756 F.2d at 1423. He was not. The record unambiguously demonstrates that Todd’s counsel had notice that the charge at issue in the second trial was sexual contact, in the form of masturbation, and not sexual intercourse. The indictment alleged that Todd engaged in “manual masturbatory contact with his penis.” During his opening statement, Todd’s counsel explained to the jury that all but two of the victims “allege[] the crime of negligently or recklessly masturbating when others are present.” He also predicted in his opening statement that the victims’ testimony would contain the following: “ ‘Yeah, he masturbated. We saw him jack off’— that's the language they are going to use— ____” Todd’s counsel raised no objections when the government questioned witnesses on the factual underpinnings of the sexual contact charges.3 Todd’s counsel cross-examined the witnesses on that testimony using a variety of materials (e.g., transcripts of Todd’s first trial, FBI notes, interviews between witnesses and other lawyers) that had certainly been prepared in advance of trial. We conclude that Todd was not deprived of his constitutionally required notice or opportunity to defend.
The fifth amendment also required that Todd be convicted only upon charges presented in an indictment returned by the grand jury. Todd invokes Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, *929273, 4 L.Ed.2d 252 (1960), which reversed a conviction for an offense not charged in the indictment. This case differs from Stirone. The grand jury indicted Stirone only on charges of extortion affecting interstate commerce in sand. He was convicted, in part, of extortion affecting interstate commerce in steel even though that charge had not been stated in the indictment. Id. at 214-17. In Todd’s case, however, the grand jury’s superseding indictment was based on testimony by FBI Special Agent John Raucci that Todd had masturbated in view of named minors, and those factual allegations were recited in the superseding indictment. Those same allegations were the subject of the trial. The superseding indictment did not deprive Todd of his fifth or sixth amendment rights.
B. Double Jeopardy
Todd argues that, because the evidence was insufficient to convict him of public “sexual intercourse” in his first trial, he cannot be retried and convicted of the charges before us. He relies on the fact that in Flores the Arizona Court of Appeals reversed a conviction for masturbation, charged as “sexual intercourse,” for insufficient evidence. Flores, 772 P.2d at 592-94. Despite the result in Flores, there are insurmountable problems with Todd’s contention.
First, our reversal on Todd’s first appeal was not based on insufficiency of the evidence, but on trial error in the admission of certain testimony. When a defendant succeeds in securing a reversal of his conviction on grounds other than insufficiency of the evidence, retrial is permissible. United States v. Scott, 437 U.S. 82, 90-91, 98 S.Ct. 2187, 2193-94, 57 L.Ed.2d 65 (1978).
Todd seeks to avoid this rule by pointing out that it is now undisputed that the evidence was insufficient to convict him of sexual intercourse for the three acts in question, because they involved only self-masturbation. Even if we were to assume,
however, that our prior reversal was tantamount to a ruling that the evidence could not support a conviction for “sexual intercourse,” the assumption would avail Todd nothing. His case would then be controlled by Montana v. Hall, 481 U.S. 400, 107 S.Ct. 1825, 95 L.Ed.2d 354 (1987). In Hall, a defendant was charged with, and convicted of, incest. The state supreme court reversed because sexual assault on the defendant’s stepdaughter did not constitute incest under the statute in force at the time of the crime. The state supreme court also held that retrial for sexual assault was barred by the double jeopardy clause. On the state’s petition for certiorari, the Supreme Court reversed the ruling that retrial was barred. The Supreme Court held that, even though a conviction for incest was insupportable, a retrial on the related charge of sexual assault was permissible. It noted that “[tjhere is no suggestion that the evidence introduced at trial was insufficient to convict respondent.” Id. at 403, 107 S.Ct. at 1827. Here, too, there is no suggestion that the evidence was insufficient to convict Todd of sexual contact, which does not require the physical participation of more than one person. Nor did the jury in the first trial, or this court on review, implicitly acquit Todd of sexual contact.4 The primary problem was that the acts that the jury was convinced that Todd had committed could not constitute public sexual intercourse under the controlling Arizona statute, although they could constitute public sexual contact.
The Supreme Court in Hall also rejected the defendant’s reliance on Brown v. Ohio, 432 U.S. 161, 97 S.Ct. 2221, 53 L.Ed.2d 187 (1977), in which the Supreme Court had held that a person convicted and punished for joyriding could not be tried subsequently on a charge of auto theft arising from the same incident. The Hall Court stated:
In Brown, the defendant did not overturn the first conviction; indeed, he served the prison sentence assessed as punishment for that crime. Thus, when *930the State sought to try him for auto theft, it actually was seeking a second conviction for the same offense. By contrast, respondent in this case sought, and secured, invalidation of his first conviction. This case falls squarely within the rule that retrial is permissible after a conviction is reversed on appeal.
481 U.S. at 404, 107 S.Ct. at 1827. Thus, even though the evidence against Todd in his first trial would not have permitted us to affirm his conviction for public sexual intercourse, the above reasoning in Hall permits Todd’s retrial on related charges of sexual contact.5 The district court did not err in rejecting Todd’s claims of double jeopardy.
C. Evidentiary Issues
Todd objects to three evidentiary rulings of the district court.
Todd contends that the district court’s exclusion of virtually all evidence relating to Fran Chapman, who allegedly had hypnotized and otherwise influenced the witnesses against Todd.6 If Todd’s evidence that Chapman used undue influence on witnesses was relevant, it was admissible subject to the ordinary rules of evidence. See United States v. Abel, 469 U.S. 45, 51-52, 105 S.Ct. 465, 468-69, 83 L.Ed.2d 450 (1984). The district court held that evidence relating to Chapman and hypnosis, even if true, was not relevant. We agree.
Todd argues that the evidence relating to Chapman was relevant to the victim-witnesses’ credibility. Todd proffered the following evidence, all of which we assume to be true in assessing its relevance: (1) Chapman was a counselor at the Grease-wood School; (2) there existed a strong animosity between Chapman and Todd; (3) Chapman provided the initial evidence which caused the FBI to commence its investigation of Todd; (4) Chapman stated at a faculty meeting that she had hypnotized students at Greasewood; (5) Chapman attempted to hypnotize one of the victim-witnesses on one occasion; and (6) Chapman was unavailable to testify at Todd’s trial. The proffered evidence would not have tended to prove that Chapman tampered with the victim-witnesses. See Fed. R.Evid. 401. Impermissible speculation unsupported by evidence would have been necessary to conclude that Chapman had actually hypnotized any victim-witness in an effort to alter the witness’ memory or testimony. The district court thus did not abuse its discretion when it excluded this evidence. See United States v. Gillespie, 852 F.2d 475, 479 (9th Cir.1988).
Todd also challenges the admission into evidence of Exhibit 22-E, a photograph found in Todd’s house of an unknown man’s genital area, and Exhibit 4-A, a photograph found in Todd’s house of a man engaged in masturbation.
As to both exhibits, it’s initially important to recognize that the jury which decided Todd’s case was not a runaway jury. The jury acquitted Todd on the most serious counts: sexual conduct with a minor and child molestation. Despite the explosive nature of the charges lodged against Todd, the jury was obviously able to separate any feelings it might have had about the events and activities alleged at trial from a rational and disinterested analysis of the evidence presented. Although this does not mean that any erroneous evidentiary ruling is necessarily harmless, it is relevant background for an assessment of the effect any such ruling had on the course of the trial.
Exhibit 22-E, the picture of an unknown male’s genitals, was offered to prove that Todd possessed an unnatural or *931abnormal sexual interest or intent with respect to children, an element of child molestation under Ariz.Rev.Stat.Ann. § 13-1410.7 United States v. Hester, 719 F.2d 1041, 1043 (9th Cir.1983). (As noted, Todd was acquitted of child molestation.) There are three possible grounds on which Exhibit 22-E might have been excluded: Fed.R.Evid. 403, Fed.R.Evid. 404 and the unreliability of the reverse Tanner Scale.8 We need not decide whether the exhibit should have been excluded on any of these three grounds; even assuming the district court erred in admitting the exhibit, the error was harmless.
If the exhibit was erroneously admitted, we must reverse unless it’s more probable than not that Todd would have been convicted on the public sexual indecency counts even had the errors not been made. See United States v. Berry, 627 F.2d 193, 201 (9th Cir.1980); see generally Haddad v. Lockheed Cal. Corp., 720 F.2d 1454, 1457 & n. 2 (9th Cir.1983) (collecting criminal cases). To make such an evaluation, we must examine the evidence that goes to the three public sexual indecency charges of which Todd was convicted. The most important is the trial testimony of three of the boys.
Jessel Kirk testified that when he was in seventh grade he watched movies at Todd’s house. He testified that on one occasion, while watching the movie Trading Places, Todd “was sitting right here, right by me and he took off his sweats and he started jacking off ... [pjlaying with his penis.” Kirk saw Todd ejaculate. While “jacking off,” Todd “touched [Kirk’s] thigh” with his arm. Herman Jim testified that he went to Todd’s house in April 1987 when he was 13, and that Todd “was jacking off.” Todd asked Herman “[i]f [he] wanted to learn how to jack off.” Herman saw Todd ejaculate, and saw the semen go into a tissue. Terry Begay testified that when he was age 13 he went to Todd’s house and watched Rocky IV. According to Begay, Todd was “packing off,” and while Todd was sitting on the couch, he instructed Begay to “[j]ack off my dick for me.” Todd also “grabbed [Begay’s] hand and touched [Todd’s] dick.”
To convict Todd of the three counts, the jury had to believe the testimony of these three boys. It obviously did. To say that the admission of Exhibit 22-E requires reversal, we must conclude that the jury would not have believed these three boys had it not seen Exhibit 22-E. The trial transcript does not permit such a conclusion.
The picture in Exhibit 22-E was a visual depiction of what the jury already knew had been found in the house, and was used mostly in an attempt to convict Todd of child molestation — obviously unsuccessfully. Two FBI agents testified about the variety of material Todd had accumulated. Agent Tonkin testified that he found the movie Boys on Film at Todd’s residence. In addition, there were magazines that showed naked young boys. Agent Raucci testified that he found photographs of naked young boys. He also found magazines and mail order material for child pornography. He found Polaroid pictures depicting Todd and depicting naked young boys. Todd does not challenge the testimony of the agents on appeal. In light of this testimony, we cannot conclude that the sight of Exhibit 22-E would have caused the jury to believe the stories of the three *932boys if it was otherwise inclined to disbelieve them.
Exhibit 4-A was a color photograph found in Todd’s house of a man sitting on a floor engaging in masturbation. In the picture, a tissue or napkin is spread on the floor beneath his penis. There is a blue rug on the floor, and the man is clothed in a rust-colored robe. Two of the alleged victims identified Todd as the person in the picture. Various of the alleged victims also testified that Todd had a rust-colored robe, that there was a blue rug in the room in Todd’s house where nearly all of the offenses were alleged to have occurred, that Todd had a Polaroid camera hanging on the wall of that room and that Todd masturbated in a specific manner into a tissue.
There were two questions about the picture: (1) Was Todd the person depicted in it; and (2) what did it prove. There was testimony by witnesses that it was Todd; the jury was thus required to determine whether those witnesses were believable and whether the witnesses had enough information to make a reliable identification given that no face appeared in the picture.
The picture showed a man with a particular masturbation style, which coincided with what various witnesses described as Todd’s. The picture depicted a rust robe, blue rug, and tissues on the floor; perhaps most importantly, the very existence of a picture evinces a willingness to masturbate in front of other persons and/or cameras, a distinctive trait. All of this combined renders the picture admissible as modus operandi evidence under Fed. R.Evid. 404(b). The district court thus did not abuse its discretion by admitting this exhibit. See United States v. Perkins, 937 F.2d 1397, 1400 (9th Cir.1991).
A limiting instruction concerning Exhibit 4-A should have been given to explicitly inform the jury that evidence of other acts, specifically the picture that allegedly depicted Todd masturbating at another time, could not be used to prove the character of Todd but only to show modus operandi. We cannot conclude, however, that the failure to give this limiting instruction constitutes reversible error. The jury must have either: (1) disregarded Exhibit 4-A because it could not determine if the picture depicted Todd or because the picture did not prove anything about the three boys’ particular stories; or (2) found that the evidence showed that Todd had a modus operandi and that the boys’ testimony meshed with that modus operandi. If the former is what occurred, no harm was done. If it was the latter, the jury made proper use of the evidence.
D. Sentencing
Todd was sentenced to ninety-nine years’ imprisonment after his first trial, including consecutive sentences of two years each for the three counts now at issue. After appeal and remand, Todd was sentenced to two and one-half years, to run consecutively, on each of the same three counts. Todd argues that he was, in effect, punished for successfully appealing. If Todd’s aggregate sentence after remand had exceeded the sentence imposed at the first trial, then we would presume that the new sentence was vindictive and, absent an adequate explanation by the district court, would strike it down as unconstitutional. United States v. Bay, 820 F.2d 1511, 1513 (9th Cir.1987). The seven and one-half year sentence imposed after Todd’s new trial clearly did not exceed the ninety-nine year sentence imposed after the first trial. The district court was not, therefore, under any obligation to explain its reasons for imposing the chosen sentence on any or all of the three counts. Bay, 820 F.2d at 1513-14. No error was committed.
CONCLUSION
We AFFIRM Todd’s conviction and sentence.
. Because the alleged crimes occurred on the Navajo Reservation and involved Indian victims, they are within federal jurisdiction. 18 U.S.C. § 1152. Because no federal statute proscribed the conduct in issue at the time it allegedly occurred, Arizona law applies under the Assimilative Crimes Act, 18 U.S.C. § 13.
. The relevant sections of Ariz.Rev.Stat.Ann. § 13-1403 state:
A. A person commits public sexual indecency by intentionally or knowingly engaging in any of the following acts, if another person is present, and the defendant is reckless about whether such other person, as a reasonable person, would be offended or alarmed by the act:
1. An act of sexual contact....
3.An act of sexual intercourse____
B. A person commits public sexual indecency to a minor if he intentionally or knowingly engages in any of the acts listed in subsection A and such person is reckless whether a minor under the age of fifteen years is present.
. Todd’s counsel objected in the district court to Count X of the superseding indictment, which inexplicably had not been changed from the original indictment to delete the phrase “an act of sexual intercourse." The district court directed a verdict of acquittal on Count X because the government had failed to demonstrate that another person, in addition to Todd, had been engaged in the acts of manual masturbation as required by Flores, 772 P.2d at 592-94. During the argument on Count X, Todd’s counsel made the following statement: “I might point out, Your Honor, that this count is different than all the other manual masturbatory counts. The other charges [sic] sexual contact. This one charges sexual intercourse." Todd’s objections to the “sexual intercourse" charge were all limited to Count X.
. The jury’s conviction of Todd for public sexual intercourse would have been an implied acquittal of the offense of public sexual contact only if the jury had been presented with both charges, and had chosen to convict Todd of public sexual intercourse. See Hall, 481 U.S. at 403 n. 1, 107 S.Ct. at 1827 n. 1. That did not occur here.
. The quoted language from Hall also defeats Todd’s attempt to rely on Grady v. Corbin, 495 U.S. 508, 110 S.Ct. 2084, 109 L.Ed.2d 548 (1990). Grady, like Brown, is clearly aimed at protecting defendants from successive prosecutions; it does not involve retrial after a successful appeal by the defendant. Grady is therefore inapplicable to our case. See Hall, 481 U.S. at 404, 107 S.Ct. at 1827.
. Todd also argues that he was denied his sixth amendment right to confront witnesses by the district court’s exclusion of evidence related to Fran Chapman. Since Chapman was not a witness at trial, either directly or through hearsay, the confrontation clause is not at issue.
. Section 13-1410 provides: "A person who knowingly molests a child under the age of fourteen years by directly or indirectly touching the private parts of such child or who causes a child under the age of fourteen years to directly or indirectly touch the private parts of such person is guilty of a class 2 felony____” Arizona courts have added a requirement of unnatural sexual interest in children to make clear that innocent contact, as by a treating physician, is not within the statute. See State v. Madsen, 137 Ariz. 16, 18, 667 P.2d 1342, 1344 (App.1983).
. Todd argues that expert testimony utilizing the Tanner Scale (a means by which doctors measure development of the penis) “backwards” did not satisfy the test for establishing the reliability of novel scientific evidence. See Gillespie, 852 F.2d at 480-81 (citing Frye v. United States, 293 F. 1013, 1014 (D.C.Cir.1923)). The claim is not without plausibility. See Daubert v. Merrell Dow Pharmaceuticals, Inc., 951 F.2d 1128, 1130 (9th Cir.1991).