Most work on relativism focuses on the debate between opponents and defenders of some relativist thesis. This article is different, for it concerns a debate among relativists as to what precise form their relativism ought to take. The main contention of this paper is modest. The main claim for which I want to argue is the claim that there is a significant difference between two broad forms a relativist thesis can take: that of indexical relativism and that of genuine relativism. This does not mean, however, that the following will be an esoteric discussion directed only at relativists. A clarification of the precise claims relativists might make will be of crucial interest to relativists and opponents alike.