Cultural pluralism assumes the persistence of inter-group conflicts and poses the question of how members of multiethnic liberal democracies should address disagreements stemming from divergent cultural values. Allowing groups greater cultural autonomy resolves some problems, but does not address those that arise when different cultural values suggest divergent answers to questions of common concern. These can be addressed through developing practices of critical intercultural dialogue that will provide a basis for mutual understanding of group values and valid intercultural criticism. Such critical intercultural dialogue is based on three criteria: the priority of understanding the other's values to criticism of them, the achievement of fair conditions of discussion, and the fostering of mutual openness and trust. This article identifies the difficulties in the way of attaining each of these criteria, drawing examples from recent discussions between members of Native American and other American communities.