In this paper we compare the orthodox optimal tariff formula with the appropriate welfare-maximizing tariff when there are a few producing or importing firms. The welfare-maximizing tariff can be very low, voire negative in some cases, while in others it can even exceed the maximum-revenue tariff. The relationship between the welfare-maximizing tariff and the number of firms need not be monotonically increasing, because the tariff is not strictly used to internalize terms of trade externality. It is also used to manipulate cost asymmetries between producing and importing firms. Welfare-maximizing specific tariffs are never worse than their ad valorem counterparts.