We ask whether offering a menu of unemployment insurance contracts is welfare-improving in a heterogeneous population. We adopt a repeated moral hazard framework as in Shavell/Weiss (1979), supplemented by unobservednheterogeneity about agents’ job opportunities. Our main theoretical contribution is an analytical characterization of the sets of jointly feasible entitlements that renders an efficient computation of these sets feasible. Our main economic result is that optimal contracts for “bad” searchers tend to be upward-sloping due to an adverse selection effect. This is in contrast to thenwell-known optimal decreasing time profile of benefits in pure moral hazard environments that continue to be optimal for “good” searchers in our model.