The theory of Power Preponderance put forward by Stephen Brooks and William Wohlforth is poised to replace structural balance-of-power theory as the leading American Realist interpretation of international politics. Power Preponderance argues that would-be rivals to the US are not balancing against it because they are dissuaded from doing so by geopolitical and structural factors, rather than because they love the US or are cowed by it. This article shows why the central analytical claim of Power Preponderance would be substantially enhanced by incorporating the logic of the nuclear revolution, but that its main policy recommendation – indefinite and magnanimous American preponderance – is undermined by the spectre of nuclear war. In the nuclear age, normative solutions to the problem of anarchy invariably gravitate toward the logic of a world state.