This paper presents a simple, basic model to compute the welfare consequences of the introduction of a tariff on the CO2 content of imported goods in a country that already imposes a domestic carbon tax. The main finding is that the introduction of a carbon import tariff increases global welfare (and not just the welfare of the importing country) if there is no (or insufficient) pricing of carbon abroad. A higher domestic price of carbon justifies a higher import tariff. Moreover, a higher relative intensity of carbon abroad increases the desirability of high import tariff imposed by the home country because a border tax shifts production to the importing country, which in this case leads to lower environmental costs. If both instruments are used to maximise global welfare, the optimal domestic price for carbon should be higher than the external effects (assuming that there is no carbon pricing in the rest of the world) and the optimal tariff rate would be somewhat lower than the domestic carbon price. If the importing country has a fixed ceiling on emissions instead of a constant carbon price (as provided under the EU's Emissions Trading System), an import tariff is always beneficial from a global point of view and its imposition lowers the price of domestic allowances, but less than proportionally.