We analyze different alternatives how a common unemployment insurance system for the euro area (EA) could be designed and assess their effectiveness to act as an insurance device in the presence of asymmetric macroeconomic shocks. Running counterfactual simulations based on micro data for the period 2000-13, we highlight and quantify the trade-off between automatic stabilization effects and the degree of cross-country transfers. In the baseline, we focus on a non-contingent scheme covering short-term unemployment and find that it would have absorbed a significant fraction of the unemployment shock in the recent crisis. However, 5 member states of the EA18 would have been either a permanent net contributor or net recipient. Our results suggest that claw-back mechanisms and contingent benefits could limit the degree of cross-country redistribution, but might reduce desired insurance effects. We also discuss moral hazard issues at the level of individuals, the administration and economic policy.