Some philosophers, like Mark Richard and Paul Boghossian, have argued against relativism that it cannot account for the possibility of faultless disagreement. However, I will contend that the objections they moved against relativism do not target its ability to account for the possibility of faultless disagreement per se. Rather, they should be taken to challenge its capacity to account for another element of our folk conception of disagreement in certain areas of discourse—what Crispin Wright has dubbed parity. What parity demands is to account for the possibility of coherently appreciating, within a committed perspective, that our opponent’s contrary judgement is somehow on a par with our own judgement. Understood in this way, Boghossian’s and Richard’s objections put indeed considerable pressure on relativism—or so I will argue. I will consider John MacFarlane’s attempt to resist their objections and I will show that, once their arguments are properly understood as targeting parity, the attempt is not successful. In the last section of the paper I will offer a diagnosis of what is at the heart of the relativist inability to account for parity—namely its assumption of a monistic conception of the normativity of truth.