In this paper, we contribute to the literature about how the welfare effects of a reduction in trade costs are impacted by market structure assumptions. We compare the Armington structure of trade under perfect competition with the Krugman structure of trade under monopolistic competition and the Melitz structure of trade under monopolistic competition with heterogeneous firms. Given its proven importance to the welfare results, we hold the local trade response (as measured in gravity regressions) constant across the model comparison exercise. We start with highly simplified versions of these models where we reproduce the result of Arkolakis et al. (2012) that the welfare impacts are identical. We then show that the welfare results of these models differ when we introduce several features that are important to real economies, several of which have not yet been examined in the literature.