How does the bargaining power of firms affect trade policy? We address this question in an international, bilateral oligopoly setting where the Home country specializes in final goods and the Foreign country specializes in intermediate inputs. A matched Home-Foreign pair bargains simultaneously over the input price and the level of output, and competes with other matched pairs in markets. In such environments with vertical specialization, we show that the welfare-maximizing Home tariff rate strictly decreases as the bargaining power of Home firms increases. Surprisingly, we find that an increase in Home bargaining power can also raises Foreign profits. These results hold for fairly general demand function and a number of different procurement mechanisms. In an endogenous market structure setting with free entry and matching, the relationship between the tariff and bargaining power is usually non-monotone. In particular, the relationship is U-shaped (resp. inverted U-shaped) if the demand function is strictly concave (resp.convex). If the demand function is linear, free trade is optimal (i.e., optimal tariff is zero) irrespective of the bargaining power. The relationship between welfare and bargaining power is also explored.