Some moral disagreements are so persistent that we suspect they are deep: we would disagree even when we have all relevant information and no one makes any mistakes (this is also known as faultless disagreement). The possibility of deep disagreement is thought to drive cognitivists toward relativism, but most cognitivists reject relativism. There is an alternative. According to divergentism, cognitivists can reject relativism while allowing for deep disagreement. This view has rarely been defended at length, but many philosophers have implicitly endorsed its elements. I will defend it.