Sovereign debt crises may be driven by either self-fulfilling expectations of default or fundamental fiscal stress. This paper studies the mechanisms by which either conventional or unconventional monetary policy can rule out the former. Conventional monetary policy is modelled as a standard choice of inflation, while unconventional policy as outright purchases in the debt market. By intervening in the sovereign debt market, the central bank effectively swaps risky government paper for monetary liabilities only exposed to inflation risk and thus yielding a lower interest rate. We show that, provided fiscal and monetary authorities share the same objective function, there is a minimum threshold for the size of interventions at which a backstop rules out self-fulfilling default without eliminating the possibility of fundamental default under fiscal stress. Fundamental default risk does not generally undermine the credibility of a backstop, nor does it foreshadow runaway inflation, even when the central bank is held responsible for its own losses.