The proliferation of preferential trade liberalization over the last 20 years has raised the question of whether it slows multilateral trade liberalization. Recent theoretical and empirical evidence indicates that this is the case even for unilateral preferences that developed countries provide to small and poor countries, but there is no estimate of the resulting welfare costs. This stumbling block effect can be avoided by replacing the unilateral preferences with a fixed import subsidy, which generates a Pareto improvement. More importantly, this paper presents the first estimates of the welfare cost of preferential liberalization as a stumbling block to multilateral liberalization. Recent estimates of the stumbling block effect of preferences with data for 170 countries and more than 5,000 products are used to calculate the welfare effects of the European Union, Japan, and the United States switching from unilateral preferences for least developed countries to an import subsidy scheme. In a model with no dynamic gains to trade, the switch produces an annual net welfare gain for the 170 countries that adds about 10 percent to the estimated trade liberalization gains in the Doha Round. It also generates gains for each group: the European Union, Japan, and the United States (,934 million), least developed countries (20 million), and the rest of the world (00 million).