SUMMARY ORDER

Defendants-Appellants Jin Kyoo Park and Myung Woo Jun appeal from a judgment of conviction entered in the District Court following a jury trial in which they were found guilty of alien smuggling in violation of 8 U.S.C. §§ 1324(a)(1)(A)(ii) and 1324(a)(2)(B)(iii). The District Court imposed, inter alia, sentences of sixteen months’ imprisonment on defendant Park and ten months’ imprisonment on defendant Jun. We assume the parties’ familiarity with the facts and the procedural history of the case.

On appeal, defendants argue that the District Court erred in (1) denying defendants’ motion to exclude statements to Border Patrol agents based on the District Court’s conclusion that defendants voluntarily waived their Miranda rights; and (2) denying defendants’ motion for a judgment of acquittal under Fed.R.Crim.P. 29 based on the District Court’s conclusion that the government need not prove the identities of the aliens smuggled by each defendant. In addition, defendant Jun argues that the District Court erred by considering conduct of which he was acquitted when imposing his sentence.

Each of defendants’ claims is without merit. First, notwithstanding the fact *76that defendants did not sign the waiver of Miranda rights presented to them during questioning, the District Court properly-found based on the facts presented that (1) defendants understood their rights when they were read aloud and translated into Korean; and (2) defendants’ subsequent statements to Border Patrol agents were made voluntarily. See North Carolina v. Butler, 441 U.S. 369, 373-76, 99 S.Ct. 1755, 60 L.Ed.2d 286 (1979) (holding that, in some cases, “waiver can be clearly inferred from the actions and words of the [defendant]”); see also United States v. Scarpa, 897 F.2d 63, 68 (2d Cir. 1990) (even absent express statement of waiver, defendant’s “relaxed and friendly” conversations contributed to a finding of waiver). Accordingly, the District Court’s decision not to exclude defendants’ statements was not error.

Second, the District Court did not err in rejecting defendants’ argument that the government must prove which of the eight aliens were smuggled by defendant Park and which were smuggled by defendant Jun. In particular, no constructive amendment of the indictment exists when, as here, the government’s failure to prove the identities of the aliens smuggled by each defendant did not alter “an essential element of the charge,” United States v. Milstein, 401 F.3d 53, 65 (2d Cir. 2005), and where the District Court’s jury instruction that no such proof was necessary constituted, at most, a harmless variance from the allegations set forth in the indictment, see United States v. Ford, 435 F.3d 204, 216 (2d Cir. 2006) (applying harmless error analysis to variances from the facts alleged in the indictment).

Finally, defendant Jun’s argument that the District Court erred by considering conduct of which he was acquitted when imposing his sentence is without merit. We have held, after Booker, that district courts may consider acquitted conduct as a factor in sentencing, see United States v. Vaughn, 430 F.3d 518, 526-27 (2d Cir. 2005), and Jun presents no persuasive argument that the District Court erred in considering such conduct.

Accordingly, we hereby AFFIRM the judgment of the District Court.