We build a stochastic model of excusable sovereign default which incorporates a simple debt recovery rule. It depends on a single parameter that allows for partial debt recovery. We show that the maximum debt-to-GDP ratio that a country can sustain without defaulting is increasing, nonlinear, and sensitive to the debt-recovery parameter. We study the dynamics of public debt when the default premium is taken into account and offer new definitions of public debt unsustainability. A higher debt recovery parameter increases the fiscal space but worsens the financial position of a borrowing country after a default episode. We show that the estimated debt-recovery parameter is lower for emerging countries than for developed countries.