Equilibrium search models generalize the one-sided models used earlier by endogenizing the wage offer distribution. Attempts to estimate versions of these equilibrium n search models have been unsuccessful, ironically because the predicted wage distribution did not fit the wage data. In this paper we extend the applicability of search models by introducing firm heterogeneity to account for the shape of the wage density. The resulting estimation problem is difficult, but we propose a solution and illustrate its feasibility and performance with a Monte Carlo study and an application to US labour market data.