This study reconstructs the concept of interstate rivalry in accordance with a min–max strategy in order to determine the necessary characteristics of rivalry, provide a template with which to assess existing conceptualizations, and provide a means by which conceptualizations of rivalry can be formulated and operationalized. I argue that there are two necessary characteristics of a minimal conceptualization of interstate rivalry — temporal dependence and issue competition. Contextual conceptualizations are then formulated by adding dimensions, such as militarization, identification, and psychological hostility, among others, to the minimal definition. By defining interstate rivalry in its most extreme form (when all of the potential dimensions of rivalry are present in the fullest), I also establish a maximal or ‘ideal-type’ conceptualization. In adopting a min–max approach, this project seeks to unify conceptualizations of interstate rivalry along a common continuum in which the empirical coverage of cases decreases as properties are added to the minimal definition.