We show that sovereign debt is unsustainable if debt contracts are not supported by direct sanctions and default carries only a ban from ever borrowing in financial markets even in the presence of uninsurable risks and time-varying interest rate. This extension of Bulow and Rogoff (1989) requires that the present value of the endowment be finite under the most optimistic valuation. We provide examples where this condition fails and sovereign debt is sustained by the threat of loss of insurance opportunities upon default, despite the fact that the most pessimistic valuation of the endowment, the natural debt limit, is finite.