Territorial disputes constitute an important root of interstate conflict. Yet these disputes do not always lead to war or even militarized conflict. Sometimes, one side yields to the other side by withdrawing its claims. Focusing on rival dyads whose territorial claims should be more intractable than is the case in non-rival dyads, we suggest that it is challengers, as opposed to the side that already controls the disputed territory in question, that are more likely to make concessions. Moreover, it is threats external to the spatial rivalry that encourage challengers to surrender their claims so that they may deal with more pressing threats. The empirical evidence supports these contentions. Territorial dispute challengers are more likely to engages in negotiations over the disputed space if they are also participants in other rivalries that, presumably, become associated with threats that are more worrisome than other, older spatial disagreements. One of several implications is that it is debatable whether we should assume that it is primarily boundary negotiations that end spatial disputes and therefore rivalries. On the contrary, the linkages between boundaries and rivalry are apt to be more complicated. Not only are all rivalries not spatial in nature, the way they end need not be due to the peaceful resolution of territorial disputes either.Findings that point to territorial disputes as among the most dangerous causes of international conflict and rivalry are well established in the interstate conflict literature. But not all territorial disputes escalate to war. Nor do all territorial disputes persist until they are resolved by coercive force. How decision-makers navigate their way out of territorial disputes is less well understood. Recourse to legal mechanisms and international law have received recent attention as key processes in efforts to reduce conflict over territory. What is left unclear is why or when decision-makers choose to make use of these legal mechanisms. Equally unclear is who makes use of opportunities to de-escalate territorial disputes. Presumably, states that are already in a rivalry relationship are less likely to walk away from a territorial dispute than states that are not rivals. There is too much psychological baggage and historical inertia to overcome in addition to dealing with the specifics of territorial control. Then, too, rivalries are often defined as manifestations of territorial disputes. Some are. Some are not. Yet, to what extent territorial disputes make rivalry more likely