A game-theoretic model is used to show that the balance-of-power mechanism has much greater formal power than hitherto understood. Under the strong assumption that all threatened countries must be able to function as crucial coalition partners in deterring any threat, all members of minimum winning coalitions are guaranteed not to lose any resources. Under the traditional, weaker assumption that some coalition must be available to deter any threat, even countries that are not members of minimum winning coalitions are guaranteed against losing any resources. These formal results are significant in two ways. First, they make it possible to reconcile apparently contradictory views in the literature, and to offer a satisfying intuitive interpretation of the balance-of- power mechanism. Second, they point to a variety of factors - operating both separately and interactively - that may cause the balance-of-power mechanism to fail. Examples are uncertainty combined with risk-loving preferences, conflict-averse preferences, offensive technological advantages, economic growth, and technological and political rigidities in the formation of alliances and rivalries. It is argued that efforts to test balance-of-power theory should focus on assessing the relative importance of such factors.