How high can public debt rise without compromising fiscal solvency? We answer this question using a stochastic model of sovereign default in which risk-neutral investors lend to a government that displays ‘fiscal fatigue’, whereby its ability to increase primary balances cannot keep pace with rising debt. As a result, the government faces an endogenous debt limit beyond which debt cannot be rolled over. Using data for 23 advanced economies over the period 1970–2007, we find evidence of a fiscal reaction function with these features, and use it to compute ‘fiscal space’, defined as the difference between current debt ratios and the estimated debt limits.