In this Article Professor Block-Lieb critically examines the power of a federal district or bankruptcy court to adjudicate jurisdictionally insufficient claims which arise out of a common nucleus of operative fact with a proceeding which ''arises under'' the Bankruptcy Code, or ''arises in'' or ''relates to'' a bankruptcy case. After considering Article III of the United States Constitution, relevant statutory provisions-including the newly enacted supplemental jurisdictional provision (28 U.S. C sectional sign 1367)-and the conflicting policy objectives of these statutory provisions, the Article concludes that a district court's adjudication of supplemental claims related to a ''related to'' proceeding may be unconstitutional, unauthorized by statute, and inconsistent with the primary purpose of bankruptcy jurisdiction-the efficient administration of a bankruptcy estate. As to a district court's exercise of jurisdiction over supplemental claims related to an ''arising under'' or ''arising in'' proceeding, it proposes that a balancing approach be adopted. It also contends that additional constitutional concerns are raised when a non-Article III bankruptcy court exercises any form of supplemental bankruptcy jurisdiction, and advocates limiting the power of bankruptcy courts accordingly.