While it is well established that across-country taste differences are associated with "home market effects", there is very limited analysis of how such preference heterogeneity impacts the aggregate volume of trade and the welfare gains from liberalization. I develop a structural model of aggregate demand featuring products with heterogeneous attributes, consumers with heterogeneous tastes for attributes, and across-country differences in the distribution of tastes. The impact of across-country taste differences depends on whether the domestic industry can adjust to the mismatch between the attribute composition of imports and the domestic distribution of tastes. For the case of a large degree of across-country taste differences, countries specialize completely and the model supports notions along the lines of Linder (1961) that taste diversity impedes the volume of trade and leads to group-specific gains from trade. In contrast, if specialization is incomplete, free firm entry implies that the relative toughness of competition across different market segments must be invariant to liberalization. It is shown that therefore, both trade volume and welfare gains are entirely unaffected by the distribution of foreign tastes and coincide with those in a representative agent framework.