Recent literature on the workhorse model of intra-industry trade has explored heterogeneous cost structures at the firm level. These approaches have proven to add realism and predictive power. This note shows, however, that this added realism also implies that there may exist a positive bilateral tariff that maximizes national and world welfare. Applying one of the simplest specifications possible, namely a symmetric two-country intra-industry trade model with fixed export costs that are heterogeneous across firms, we find that the reciprocal reduction of small tariffs reduces welfare.