We propose a redesign of sovereign Credit Default Swaps (CDS). Under our proposal, a notional CDS position of €100 can be settled by the delivery of whatever package of instruments a sovereign gives in exchange for legacy bonds with a face value of €100. To illustrate, suppose a European sovereign restructures its debt by forcibly exchanging each €100 principal of legacy bonds for €50 principal of new bonds. In this case, our proposal would allow a notional CDS position of €100 to be settled by the delivery of new bonds with a principal of €50. We show that CDS protection payouts would then reflect actual losses to bondholders. We explain why the current CDS contract design fails this test, sometimes perversely, with adverse consequences for hedging performance and price discovery.