In a group of countries like the European Union all countries seek to achieve their national CO2 emissions target by a joint emissions trading scheme covering some part of their economies (trading sector) and by a national emissions tax in the rest of their economies (nontrading sector). Applicable are also emissions taxes overlapping with the trading scheme that can either be freely chosen or are inert. Welfare-maximizing governments determine tax rates and the tradable-permits budget. It is shown that efficiency requires not to levy overlapping emissions taxes and to set the tax rate in the nontrading sector equal to the permit price. In the small-country case emissions control turns out to be efficient if tax rates in the trading sector are flexible. Otherwise it is second-best to violate cost effectiveness and to choose an excessive endowment of tradable permits. If countries are large and optimal tariffs cannot be applied, emissions taxes or subsidies (!) are shown to serve as a perfect surrogate; efficiency cannot be attained unless there is a central authority mandating cost effectiveness and banning overlapping taxes. Fiscal externalities are specified and the countries' welfare in the large and small country case is compared.