We use the Ramsey and Mirrlees approaches to study how fiscal and trade policy should be set cooperatively when governments must raise revenues with distorting taxes. Free trade and unrestricted capital mobility are optimal. Efficient outcomes can be implemented with taxes only on final consumption goods and labor income. We study alternative tax systems, showing that uniform taxation of household asset returns, and not taxing corporate income yields efficient outcomes. Border adjustments exempting exports from and including imports in the tax base are desirable. Destination- and residence-based tax systems are desirable compared to origin- and source-based systems.