According to many philosophers, rationality is, at least in part, a matter of one’s attitudes cohering with one another. Theorists who endorse this idea have devoted much attention to formulating various coherence requirements. Surprisingly, they have said very little about what it takes for a set of attitudes to be coherent in general. We articulate and defend a general account on which a set of attitudes is coherent just in case and because it is logically possible for the attitudes to be jointly satisfied in the sense of jointly fitting the world. In addition, we show how the account can help adjudicate debates about how to formulate various rational requirements.