We present robust evidence on the presence of adverse selection in hospitalization insurance for low-income households. A large randomized control trial from Pakistan allows us to separate adverse selection from moral hazard, to estimate how selection changes at different points of the demand curve and to test simple measures against adverse selection. The results reveal substantial selection in individual policies, leading to welfare losses and the threat of a market breakdown. Bundling insurance policies at the household or higher levels almost eliminates adverse selection, thus mitigating its welfare consequences and creating the possibility for sustainable insurance supply.