We consider a model of a trading world consisting of an arbitrary number of nations engaged in international trade in an arbitrary number of commodities. Starting from an arbitrary tariff-distorted initial equilibrium, we examine the possibilities of undertaking a gradual multilateral reform of tariffs (and other trade taxes and subsidies) so as to attain a strict Pareto improvement in welfare. Necessary and sufficient conditions for the existence of strict Pareto-improving multilateral (differential) tariff reforms, accompanied by international transfers of income, are obtained. These results are then applied to various concrete tariff reform proposals such as proportional reductions in tariffs and the reduction of the highest ad valorem tariff rates. Some of our theorems extend the generality of previously obtained results, and some new tariff reform proposals are also made.