Recently a number of writers have argued that a new form of relativism involves a form of semantic context-dependence which helps it escape the perhaps most common objection to ordinary contextualism; that it cannot accommodate our intuitions about disagreement. I argue: (i) In order to evaluate this claim we have to pay closer attention to the nature of our intuitions about disagreement. (ii) We have different such intuitions concerning different questions: we have more stable disagreement intuitions about moral disputes than about, say, disputes about matters of taste. (iii) The new form of relativism does not vindicate the stable intuitions about disagreement. (iv) It does a better job explaining the unstable intuitions than contextualism. But, pace some relativists, it is not clear that assertion-truth rather than just proposition-truth has to be relativized to accomplish this.