Why do some parties fail to settle conflict, even after long periods of fighting? Bargaining theory explains this through imperfect information, commitment problems, war entrepreneurs, and indivisible stakes. Integrating insights from social psychology into bargaining theory, this article proposes an additional bargaining obstacle. Conflict party members not only care about their in-group's welfare, but also want to avoid rewarding their opponent through concessions. A mutually acceptable agreement always contains concessions, yet when concessions are unpopular with key constituents, they are costly for leaders to make. This may result in a situation where leaders would prefer to settle but still decide to continue the war. Modifying a standard bargaining setup to account for this dilemma, the article demonstrates the difficulties of settling a conflict when out-group preferences are salient. It shows how events that increase the saliency of out-group preferences, such as major ceasefire violations, lead to a drop in public support for negotiations. The problem of costly concessions renders the search for a mutually acceptable agreement a delicate balancing act, particularly if constituents are isolated from the costs of war and political competitors mobilize around unpopular concessions.