In the United States v. Alvarez Machain, the United States Supreme Court held that the United States could exercise criminal jurisdiction over a Mexican doctor who was abducted by agents of the American government from his office in Mexico and transported to the United States. As the Court's first international law decision after the end of the cold war, this case set the stage for how it would approach the domestic application of international law in the post cold war era. Despite the importance of the case, the Supreme Court failed to articulate the conceptual understanding of the relationship between the domestic and international orders which led it to disregard international law. Working from the author's own positivist theory of the relationship between the domestic and international realms, he explains why the decision lacks conceptual coherence and offers a structured analysis which leads to the conclusion that the Court should have applied the international law of jurisdiction.