Realism explains the ruling of the international system through the underlying distribution of power among states. Increasingly, analysts have found this power analysis inadequate, and they have developed new concepts, most prominently structural power. The usage of structural power actually entails three different meanings, namely indirect institutional power, nonintentional power, and impersonal power. Only the first, however, is compatible with the current neorealist choice-theoretical mode of explanation. This is the basic paradox of recent power approaches: by wanting to retain the central role of power, some international relations and international political economy theory is compelled to expand that concept and to move away from the very theory that claims to be based on power. Neorealism does not take power seriously enough. At the same time, these extensions of the concept are themselves partly fallacious. To account simultaneously for the different meanings of structural power and to avoid a conceptual overload, this article proposes that any power analysis should necessarily include a pair or dyad of concepts of power, linking agent power and impersonal governance. Finally, it sketches some consequences of those concepts for international theory.