SUMMARY ORDER

Following a jury trial, defendant Mark Friedman was convicted of one count of utilizing the internet in an attempt to entice a minor to engage in sexual activity, in violation of 18 U.S.C. § 2422(b), and one count of traveling interstate for the purpose of engaging in sexual activity with a minor, in violation of 18 U.S.C. § 2423(b). Defendant was sentenced principally to a term of imprisonment of 81 months on each count, with sentences to run concurrently. Defendant contends that the evidence was insufficient to prove that he had sexual contact with the minor victim. He contends also that it was prejudicial error to admit nude photographs of him into evidence and to limit his cross-examination of the minor victim, and that the District Court violated his Sixth Amendment rights when it sentenced him under the United States Sentencing Guidelines, based on facts neither found by a jury nor admitted by the defendant.

The first claim, as to the sufficiency of the evidence, is without merit. It is sufficiently answered by the fact that the fourteen-year-old victim, “Cindy,”1 testified at trial that sexual touching did occur. In any case, neither § 2422(b) nor § 2423(b) requires as an element that sexual contact have actually occurred. Under § 2422(b), the offense is committed when a person “using the mail or any facility or means of interstate or foreign commerce ... knowingly persuades, [or] induces ... any individual who has not attained the age of 18 years, to engage in ... any sexual activity for which any person can be charged with a criminal offense, or attempts to do so.” (emphasis added). The offense under 2423(b) is committed when a person “travels in interstate commerce ... for the purpose of engaging in any illicit sexual conduct with another person.” As the government’s evidence was sufficient to prove that the defendant used internet messages in an attempt to induce a fourteen-year-old to engage in covered sexual activity and that he traveled in interstate commerce for the purpose of engaging in illicit sexual contact with a fourteen-year-old, the evidence was sufficient regardless of whether sexual touching in fact occurred.

The claim of unfair prejudice for the receipt in evidence of nude photographs of the defendant is without merit. The District Court determined that the pictures, which were on Friedman’s digital camera in the car during his meeting with Cindy, were relevant evidence of his culpable intentions. We agree. For example, one photograph, together with Cindy’s testimony that it was emailed to her by the defendant, tended to show that the defendant was attempting to induce Cindy to have sex with him. Another photo found on his camera, depicting him in an aroused state, could be determined by the television in the background to have been taken during the morning just preceding his appointment to meet with Cindy, and thus evidenced his sexual intentions at that time. We find no error in the District *333Court’s ruling. See United States v. Abreu, 342 F.3d 183, 190 (2d Cir. 2003).

Friedman’s third argument, that his cross-examination of Cindy was improperly curtailed, calls for more discussion. Material found on Cindy’s computer revealed that, prior to her meeting with the defendant, Cindy had engaged in a sexually provocative exchange with another instant message correspondent, who identified himself as a boy. Her computer files also included sexually explicit pictures of naked men.

Before the start of trial, at the government’s instance, the District Court ruled in limine provisionally barring the defendant from introducing such evidence of Cindy’s sexual predisposition. The government’s argument supporting this ruling was made in part under Fed.R.Evid. 412 which, in cases involving charges of sexual misconduct, generally bars evidence offered to prove the victim’s sexual predisposition and sexual behavior.

Apparently relying on the protection of this pretrial ruling, the government, during its direct examination of Cindy, asked questions irrelevant to the elements of the charge, which were designed to project a somewhat misleading picture of Cindy as a child who had no interest in sex. The defendant had sent Cindy a naked side view photograph of himself, which did not show his genitals, asking her how she liked his picture. She responded, “i like it ... but one thing .. i cant see your cock.” Although the defendant’s culpability did not turn in any way on the intentions or sexual sophistication of the minor victim, the AUSA asked her the irrelevant question, “[Cindy], why would you say that to him? ... Did you know what it meant?” Cindy denied that at the time of the message she knew the meaning of the word.2

Another such episode occurred when Cindy testified that, after she and the defendant got into his car, they touched each other sexually. The AUSA then asked her the irrelevant but tactically significant question whether she enjoyed the touching. When she answered, “No,” the AUSA followed by asking, “Did you like it a little?”-again eliciting a “No” answer.

Because Cindy was under age, whether she consented or indeed solicited the sexual encounter, whether she knew about sex and whether she enjoyed it, were irrelevant to the defendant’s guilt. Apart from being irrelevant, Cindy’s assertions, especially of not knowing the meaning of the word, were quite suspect, given her apparently well-informed use of the word in her instant message exchanges.

Following this direct examination, the defense sought leave to impeach this line of testimony in part by reference to the naked photographs on her computer and her exchange with the boy-correspondent in which she had also used the word as a clear sexual reference. The government opposed the application.

The District Court recognized that the government had opened the door, requiring some revision of the pretrial ruling excluding the evidence of the sexual nature of Cindy’s computer files. The Court relaxed its earlier ruling, allowing the defendant to ask Cindy some impeaching questions, but did not allow the full latitude the defense was seeking. The defendant’s claim on appeal protests the restrictions on *334cross-examination which the Court left in place.

While it is arguable, especially given the prejudicial manner in which the government introduced the issue, that the Court might have given the defense somewhat wider leeway to impeach the witness on these matters, we cannot say that its ruling, seeking a fair compromise of allowing reasonable impeachment while preventing diversion of the trial into a test of the victim’s sexual proclivities, was error. The Court allowed significant questioning to impeach the witness, and she was substantially impeached.

Furthermore, regardless of whether the restrictions on cross-examination were error under the Confrontation Clause, we are persuaded that the result was harmless beyond a reasonable doubt and thus passed the test of Delaware v. Van Arsdall, 475 U.S. 673, 684, 106 S.Ct. 1431, 89 L.Ed.2d 674 (1986); see also Bern v. Greiner, 402 F.3d 100, 106-07 (2d Cir. 2005). The evidence of the defendant’s guilt, even without Cindy’s testimony, was extremely strong. It included the testimony of the shopping mall guard who interrupted the defendant and Cindy in his car, the defendant’s instant messages to Cindy that upon their meeting he wanted her to see him in an aroused state, and the condoms the defendant had with him in his car. The defendant’s sexual intentions were overwhelmingly proved. Certain key details of Cindy’s testimony were corroborated. And as to other, less critical portions of her testimony, she was very effectively impeached by the expanded examination the district judge did allow, in which Cindy virtually admitted having lied in several respects. Even if the disputed impeachment had been allowed, we think it clear beyond a reasonable doubt that Friedman would have been found guilty. Id. For the foregoing reasons, the finding of guilt is affirmed.

Friedman also contends on appeal that the District Court’s application of the United States Sentencing Guidelines violated his Sixth Amendment rights. See United States v. Booker, 543 U.S. -, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). We agree, and remand for reconsideration of the sentence as directed in United States v. Crosby, 397 F.3d 103 (2d Cir. 2005).