This paper studies the welfare implications of trade opening in a world in which trade raises aggregate income but also increases income inequality, and in which redistribution needs to occur via a distortionary income tax-transfer system. We provide tools to characterize and quantify the effects of trade opening on the distribution of disposable income (after redistribution). We propose two adjustments to standard measures of the welfare gains from trade: a `welfarist' correction inspired by the Atkinson (1970) index of inequality, and a `costly-redistribution' correction capturing the efficiency costs associated with the behavioral responses of agents to trade-induced shifts across marginal tax rates. We calibrate our model to the United States over the period 1979-2007 using data on the distribution of adjusted gross income in public samples of IRS tax returns, as well as CBO information on the tax liabilities and transfers received by agents at different percentiles of the U.S. income distribution. Our quantitative results suggest that these corrections are nonnegligible: trade-induced increases in inequality of disposable income erode about 20% of the gains from trade, while the gains from trade would be about 15% larger if redistribution was carried out via non-distortionary means.