The proliferation of preferential trade liberalization over the last 20 years has raised the question of whether it slows down multilateral trade liberalization. Recent theoretical and empirical evidence indicates 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. To avoid this stumbling block effect we suggest replacing unilateral preferences by a fixed import subsidy. We argue that this scheme would reduce the drag of preferences on multilateral liberalization and generate a Pareto improvement. More importantly, we provide the first estimates of the welfare cost of preferential liberalization as a stumbling block to multilateral liberalization. By combining recent estimates of the stumbling block effect of preferences with data for 170 countries and over 5,000 products we calculate the welfare effects of the United States, European Union and Japan switching from unilateral preferences to Least Developed Countries to the import subsidy scheme. Even in a model with no dynamic gains to trade we find that the switch produces an annual net welfare gain for the 170 countries ($4,354 million) and for each group: the United States, European Union and Japan ($2,934 million), Least Developed Countries ($520 million) and the rest of the world ($900 million).