The addition of new issues and parties to negotiations is often recommended as a means of conflict management at the international level. Such addition (or "negotiation arithmetic") contains an element of strategic interaction that is often ignored in the prescriptive work on conflict management. Though disputants in an international crisis may be seeking to avoid war, they are also trying to protect important national interests. For that reason, each disputant has an incentive to choose only those options that make her better off. Since what makes one disputant better off may make the other disputant worse off, conflict management is necessarily a matter of strategic choice. A game-theoretic analysis of disputants' incentives to pursue the conflict management options of issue linkage and mediation demonstrates that these strategies are complementary. The conditions that preclude the pursuit of one strategy encourage the pursuit of the other. Empirical tests of the resulting hypotheses indicate that the more likely a dispute dyad is to pursue mediation, the less likely it is to pursue issue linkage.