The principle of alternative possibilities (PAP) says that doing something freely implies being able to do otherwise. I show that Descartes consistently believed not only in PAP, but also in clear and distinct determinism (CDD), which claims that we sometimes cannot but judge true what we clearly perceive. Because Descartes thinks judgment is always a free act, PAP and CDD seem contradictory, but Descartes consistently resolved this apparent contradiction by distinguishing between two senses of 'could have done otherwise.' In one sense alternative possibilities are necessary for freedom and in another they are not. I discuss three possible interpretations of the two senses.