I examine issues in the philosophy of religion at the intersection of what possibilities there are and what a God, as classically conceived in the theistic philosophical tradition, would be able to do. The discussion is centered around arguing for an incompatibility between theism and two principles about possibility and ability, and exploring what theists should say about these incompatibilities. -/- I argue that theism entails that certain kinds and amounts of evil are impossible. This puts theism in conflict with (...) popular principles of modal recombination. However, theists have plausible explanations for the violations of recombination that they posit, and can suitably amend these principles without giving up their usefulness in accounting for what possibilities there are. -/- I also argue that despite the impossibility of these evils, God is able to bring these evils about. This puts theism in conflict with the principle that no one is able to do the impossible. However, theists can give a plausible account of why God is unique in being able to do the impossible, and have distinctive resources to address the arguments in favor of the idea that no one is able to do the impossible. And by denying this principle, theists are able to resolve several otherwise difficult puzzles, including reconciling conflicts between the divine attributes. (shrink)