Most accounts of the power of Congress over the appellate jurisdiction of the Supreme Court focus on the Exceptions and Regulations Clause and the degree to which it authorizes Congress to restrict the Court's role as the ultimate interpreter of federal law. [This Article] proposes to broaden the debate over jurisdiction stripping to include a consideration of the constitutional significance of the Court's required "supremacy." Beginning with the text of Articles I and III, [the Article] notes the requirement that any federal courts that Congress creates must remain "inferior" to the one Supreme Court that the Constitution itself requires. [It] shows that the framers of the Constitution were likely to have understood the required relationship of supremacy and inferiority to entail a power in the Supreme Court to supervise lower courts through the issuance of the supervisory writs of mandamus, prohibition, and habeas corpus. Building on this supervisory understanding of the Court's supremacy, [the Article] reviews the historical and doctrinal case for a constitutional power of supervision. Finding broad support for such a power in the adoption and interpretation of the statutory precursors of the modern All Writs Act, [it] concludes that Congress may not place the work of lower federal courts beyond the supervisory authority of the Court.