Petitioner Robert E. Detrich, convicted of importation of heroin in violation of 21 U.S.C. § 952(a) (1988), appeals from an order of the United States District Court for the Eastern District of New York, Edward R. Korman, Judge, denying his petition to vacate his conviction on grounds of collateral estoppel and double jeopardy. For the reasons below, we affirm.

Detrich was originally charged with importation of heroin, possession of heroin with intent to distribute, and conspiracy to possess heroin. At his first trial, he was acquitted on the possession and conspiracy counts but was convicted on the importation count. This is Detrich’s third trip to this Court with respect to his conviction for importation.

In his first appeal, we reversed and remanded for a new trial of the importation charge because evidence offered by Detrich had been improperly excluded. See United States v. Detrich, 865 F.2d 17, 20-21 (2d Cir.1988) (“Detrich I”). Convicted after retrial, Detrich appealed again, contending, inter alia, that, in light of his acquittal on the possession and conspiracy charges, his retrial and new conviction violated principles of double jeopardy and collateral es-toppel. We rejected those contentions, and others, and affirmed. See United States v. Detrich, 895 F.2d 1410 (2d Cir.1989) (“Detrich II”). The present appeal involves Detrich’s postconviction petition to vacate his conviction principally on grounds of collateral estoppel and double jeopardy. To the extent that these arguments were made in Detrich II, we decline to address them again.

In addition to the arguments made in Detrich II, Detrich now relies principally on the Supreme Court’s recent decision in Grady v. Corbin, — U.S.-, 110 S.Ct.[*480] 2084, 109 L.Ed.2d 548 (1990), for the proposition that he could not be retried after Detrich I. Detrich’s reliance is misplaced.

In Detrich I, though we found there had been an error in the trial court’s exclusion of evidence proffered by Detrich, we found the government’s evidence sufficient to support his conviction for importation of heroin. In accordance with long-accepted principles, we remanded for a new trial. “It has long been settled ... that the Double Jeopardy Clause’s general prohibition against successive prosecutions does not prevent the government from retrying a defendant who succeeds in getting his first conviction set aside ... because of some error in the proceedings leading to conviction.” Lockhart v. Nelson, 488 U.S. 33, 38, 109 S.Ct. 285, 289, 102 L.Ed.2d 265 (1988); see United States v. Tateo, 377 U.S. 463, 84 S.Ct. 1587, 12 L.Ed.2d 448 (1964); United States v. Ball, 163 U.S. 662, 16 S.Ct. 1192, 41 L.Ed. 300 (1896); see also Lockhart v. Nelson, 488 U.S. at 34, 39, 109 S.Ct. at 287, 290 (retrial permitted so long as evidence at first trial was sufficient to support conviction). In Nelson, the Court described this rule as “a ‘well-established part of our constitutional jurisprudence,’ ... [that] is necessary in order to ensure the ‘sound administration of justice’.” Id. at 38, 109 S.Ct. at 289 (quoting United States v. Tateo, 377 U.S. at 465, 466, 84 S.Ct. at 1588, 1589).

In Grady v. Corbin, 110 S.Ct. 2084, the Supreme Court set forth a test to be used to determine when principles of double jeopardy are violated by successive separate prosecutions. It did not purport to make its new standard applicable to separate charges within a single prosecution. See United States v. Maldonado-Rivera, 922 F.2d 934, 981 (2d Cir.1990). The Cor-bin Court did not mention Nelson, Tateo, Ball, or any other case dealing with the permissibility of retrial on remand after a successful appeal, and we do not view Cor-bin as disturbing the principle, so necessary to “the ‘sound administration of justice’,” that, so long as the evidence at the first trial was sufficient to support the conviction, retrial after a successful appeal is permissible.

The order of the district court denying Detrich’s petition is in all respects affirmed.