We present evidence of inelastic demand for risky sovereign bonds and explore its implications for optimal government debt policies. Using monthly changes in the composition of a major international bond index, we identify flow shocks unrelated to fundamentals that shift the available bond supply. From these shocks, we estimate an inverse demand elasticity of -0.30 and show that it increases with countries’ default risk. We formulate a sovereign debt model with endogenous default and inelastic investors, calibrated to our empirical estimates. By penalizing additional borrowing, an inelastic demand acts as a disciplining device that reduces default risk and bond spreads.