This Paper presents a new theoretical framework for understanding how insolvent foreign nation-states work out their defaulted debts. "Sovereign debt restructuring," as the process is known, is of critical importance to the dozens of developing countries around the world who have borrowed over 1 trillion dollars under the law of the State of New York and other jurisdictions. It explains how and why the prevailing system of sovereign debt restructuring works even though it operates informally and is based on voluntary, out-of-court negotiations supported by the inclusion of voting clauses in sovereign bonds to bind-in holdout creditors ("Collective Action Clauses"). The theory of sovereign debt restructuring is introduced through a review of the famous 2001 and 2003 policy debates (known as "the CAC-SDRM debate") that pitted the U.S. Treasury, which favored the voluntary, contract-based approach based approach that is used today against the International Monetary Fund ("I.M.F."), which favored the adoption of a formal, treaty-based, Chapter-11-like statutory scheme, which it called a Sovereign Debt Restructuring Mechanism ("SDRM"). Material from these debates plus additional insights borrowed from the theory of corporate insolvency, the doctrine of sovereign immunity, and financial history are then used to argue that a workable system must be based on the voluntary participation of the sovereign and other stakeholder groups. This Paper sets out design principles for designing a workable voluntary sovereign debt restructuring system and presents a model of how the various parties and processes are effectively coordinated. This Paper concludes with the proposal of two incremental reforms to help fill observed gaps in the prevailing system: (i) an expansion of existing statutory stay powers to limit to the potential for disruption of out-of-court negotiations brought by uncooperative creditors; and (ii) a limitation on payment-blocking injunctions like the one granted in the Argentina bond litigation that led to a fresh default on 30 billion dollars of performing, but previously-restructured bonds.