Sanctions are measures that one party (the sender) uses to influence another (the target). Sanctions, or the threat of sanctions, have been used by governments to alter the human rights, trade, or foreign policies of other governments. We develop notions of the sender's and target's toughness that depend on their patience and on the extent of their suffering from sanctions. How much a sender can exact from the target depends on the relative toughness of the two. Sanctions that impose less harm on the target can sometimes be more effective than those that impose greater harm.