Public disability insurance (DI) programs in many countries face pressure to reduce their generosity in order to remain sustainable. In this paper, we investigate the welfare effects of giving a larger role to private insurance markets in the face of public DI cuts. Exploiting a unique reform that abolished one part of the German public DI system for younger workers, we find that despite significant crowding-in effects, overall private DI take-up remains modest. We do not find any evidence of adverse selection on unpriced risk. On the contrary, private DI tends to be concentrated among high-income, high-education and low-risk individuals. Using a revealed preferences approach, we estimate individual DI valuations, a key input for welfare calculations. We find that observed willingness-to-pay of many individuals is low, such that providing DI partly via a private insurance market with choice improves welfare. However, we show that distributional concerns as well as individual risk misperceptions can provide grounds for justifying a full public DI mandate.