We analyse the effect of skill mismatch in a search model of equilibrium unemployment with risk-neutral agents, endogenous job destruction, and two-sided ex-ante heterogeneity. First, we examine the interaction of labour market institutions and skill mismatch. We find that skill mismatch changes the results obtained in a model with ex ante homogeneity. Second, we analyse the interaction of skill mismatch and labour market institutions for the difference in the labour market experience of continental Europe on the one hand and the US on the other hand. We find that within-group skill mismatch cannot explain the rise in unemployment in Europe relative to the US. This result is due to the endogeneity of job destruction and stands at odds with previous findings in the literature. We can, however, confirm the fact that unemployment benefits potentially play a beneficial role by providing a subsidy to search. Generally, we argue that in search models with fixed match characteristics, job destruction should be endogenised in order to take account of heterogenous decision rules.