This working paper deals with the claim that the decline of multilateralism is but a logical outcome of the present distribution of international power. In a first part, it analyses a double causal claim, namely that the distribution of international power (unipolarity) determines the nature of US foreign policy (primacy-plus-unilateralism) which is antithetical to multilateralism as an institution. On the basis of recent conceptual analyses of power, which challenges the assumptions necessary to make such aggregate power analysis, I argue that the general thesis of a causal relationship between unipolarity and a decline of multilateralism does not hold. A second part argues applies a constructivist twist to the conceptual analysis of power in order to assess whether a particular conception of power, if shared, has an actual effect on world order. Precisely because the distribution of power resources does not determinate outcomes, but are often understood to do so, the capacity to shape the definitions of power is not mere semantics, but has political effect. This move reverses the relationship between the two central concepts. Rather than seeing unprecedented preponderance as the cause of unilateralism, it shows how a successful (neoconservative) policy of US unilateralism could foster a certain understanding of power which, if it becomes shared by the international society, will have real power effects akin to the alleged effects of unipolarity.