Jean L Cohen’s impressive new volume argues that the existing global order’s own internal attributes point the way to the possibility of attractive as well as realistic institutional reforms. Global dualism, she argues, suggests the advantages of constructing non-statist global federations, in which sovereign states would cooperate in far-reaching ways to tackle common problems, in conjunction with a ‘low-intensity’ – yet potentially path-breaking – constitutionalization of global governance. If properly achieved, such reforms could produce a global order better able to preserve legality, protect rights, and allow for far-reaching political autonomy. This review chiefly focuses on the author’s attempt to link her normative and political ideas, and especially her ideas about constitutional pluralism and global federations, to her analysis of the existing global order. Despite the many virtues of her reform ideas, they sometimes embody unfairly hostile views of cosmopolitan political and legal aims. Unfortunately, Cohen has not sufficiently responded to political and institutional cosmopolitans who seek potentially more far-reaching alterations to our global order than she deems desirable.