Sovereign debt is not sustainable even in the presence of uninsurable risks; which extends the result of Bulow and Rogoff (1989). But the argument is not as general. Indeed, examples show that positive borrowing may be enforced even though the sovereign’s natural debt limits, corresponding to the most pessimistic evaluation of future endowment, are finite. Unsustainable sovereign debt in incomplete asset markets requires a strong version of high implied interest rates: the value of the most optimistic evaluation of future endowment is finite