Questions about norm diffusion in world politics are not simply about whether and how ideas matter, but also which and whose ideas matter. Constructivist scholarship on norms tends to focus on "hard" cases of moral transformation in which "good" global norms prevail over the "bad" local beliefs and practices. But many local beliefs are themselves part of a legitimate normative order, which conditions the acceptance of foreign norms. Going beyond an existential notion of congruence, this article proposes a dynamic explanation of norm diffusion that describes how local agents reconstruct foreign norms to ensure the norms fit with the agents' cognitive priors and identities. Congruence building thus becomes key to acceptance. Localization, not wholesale acceptance or rejection, settles most cases of normative contestation. Comparing the impact of two transnational norms on the Association of Southeast Asian Nations (ASEAN), this article shows that the variation in the norms' acceptance, indicated by the changes they produced in the goals and institutional apparatuses of the regional group, could be explained by the differential ability of local agents to reconstruct the norms to ensure a better fit with prior local norms, and the potential of the localized norm to enhance the appeal of some of their prior beliefs and institutions.