This paper uses a numerical general equilibrium model to examine the quantitative importance of pre-existing factor tax distortions for the welfare effects of restrictive trade policies in economies with and without market power in trade. We analyze tariffs, nonauctioned import quotas (with rents accruing to domestic firms) and voluntary export restraints (with rents accruing to foreign firms). We find that allowing for interactions with pre-existing taxes can greatly magnify the overall costs of these policies, f{fn possibly by over several hundred percent! In the case of import tariffs, much of this additional cost can be offset if the tariff revenues are used to reduce other distortionary taxes. Indeed the cost discrepancy between revenue-neutral tariffs and import quotas is dramatic at modest levels of import reduction, but declines to zero as these policies become prohibitive. We find that the optimal tariff for a country with market power in trade is greatly reduced, and possibly to zero, unless tariff revenues finance cuts in other distorting taxes. The proportionate increase in costs due to pre-existing taxes is much smaller under voluntary export restraints than under import quotas when costs are measured by domestic welfare losses, but not when measured by world welfare losses.