Empirical evidence supports the poliheuristic (PH) theory of decision making, which states that leaders typically employ a two-stage non-compensatory decision-making process. In stage one leaders reject options that do not meet some minimum criteria of acceptability on one or more dimensions, and in stage two they choose among the remaining options using a more rational utility-maximizing rule. While PH theory has primarily been applied at the monadic level, to explain the process and content of states’ decisions, we contend it has important implications for strategic interaction and can help to explain outcomes in world politics. Specifically, we argue that a crucial variable shaping crisis outcomes is the degree to which leaders’ non compensatory decision criteria in stage one include options’ acceptability to the opponent. When leaders empathize with their opponent and screen out those options the opponent considers unacceptable, crises will be resolved more quickly and with a lower likelihood of escalation. Empathy introduced during the second, utility-maximizing stage, may also dampen conflict but is less effective than stage one empathy. We illustrate this dyadic non compensatory model by examining two cases involving the U.S.–China and U.S.–Iraq bilateral relationships.