We discuss how standard computable equilibrium models of trade policy can be enriched with selection effects without missing other important channels of adjustment. This is achieved by estimating and simulating a partial equilibrium model that accounts for a number of real world effects of trade liberalisation: richer availability of product varieties; tougher competition and weaker market power of firms; better exploitation of economies of scale; and, of course, efficiency gains via the selection of the most efficient firms. The model is estimated on E.U. data and simulated in counterfactual scenarios that capture several dimensions of European integration. Simulations suggest that the gains from trade are much larger in the presence of selection effects. Even in a relatively integrated economy as the E.U., dismantling residual trade barriers would deliver relevant welfare gains stemming from lower production costs, smaller markups, lower prices, larger firm scale and richer product variety. We believe our analysis provides enough ground to support the inclusion of firm heterogeneity and selection effects in the standard toolkit of trade policy evaluation.