Trade sanctions are a common instrument of diplomatic retaliation. To guide current and future policy, we ask: What is the most cost-efficient way to impose trade sanctions? To answer this question, we build a quantitative model of international trade with input-output connections. Sanctioning countries simultaneously choose import tariffs to maximize their income and to minimize the income of the sanctioned country, with different weights placed on these objectives. Applying the model to the recent debate of sanctions against Russia, we find, first, that for countries with a small willingness to pay for sanctions, the most cost-efficient sanction is a uniform, about 20% tariff against all products. Second, if countries are willing to pay at least USD 0.7 for each USD 1 drop in welfare of the sanctioned country, an embargo on mining and energy products—with tariffs above 50% on other products—is the most cost-efficient policy.