We study the competitive and reallocation effects of trade opening in monopolistic competition. To this purpose, we generalize the Melitz (2003) setup with heterogeneous firms and fixed and variable trade costs beyond the CES to the case of additively separable utility functions. We find that extensive margin (Melitz-type selection) effects are robust to relaxing the CES assumption. Intensive margin effects (market share reallocations across inframarginal firms) and competitive (markup) effects are instead fragile. An important implication is that measured productivity gains from trade opening are no longer ensured with non-CES preferences. We discuss our results in the light of alternative setups featuring non-additive preferences, strategic interaction and consumers' preference for an ideal variety.