This Article challenges the prevailing doctrinal, political, and academic view that the Extension Clause—which provides that “[t]he judicial Power shall extend” to nine types of cases and controversies—justifies legislative attempts to strip the U.S. Supreme Court of appellate jurisdiction. Legislators have repeatedly introduced bills seeking to prevent the Court from hearing cases on politically charged topics such as marriage, religion, and abortion. Scholars have relied on the Extension Clause to advance three arguments in support of such jurisdiction-stripping: (1) that “judicial Power” is not jurisdiction, and thus jurisdiction is not constitutionally protected; (2) that “shall” is not mandatory, and thus the clause need not be obeyed; and (3) that to “extend” a power is not to grant it but merely to define its potential outer reaches, and thus Congress is responsible for deciding what to allow the Court to hear. As the Article explains, however, the text, context, and drafting history of the Extension Clause reveal the fallacy of those conventional justifications. Just as other constitutional provisions guarantee the jurisprudential independence of federal judges so that they can do their jobs without fear of reprisal, the Extension Clause prevents Congress from taking certain cases away from the Supreme Court and thus secures the Court’s jurisdictional independence.