In recent attempts at deriving morality from rationality expected utility theory has played a major role. In the most prominent such attempt, Gauthier'sMorals by Agreement, a mode of maximizing utility calledconstrained maximization is defended. I want to show that constrained maximization or any similar proposal cannot be coherently supported by expected utility theory. First, I point to an important implication of that theory. Second, I discuss the question of what the place of constrained maximization in utility theory might be. Third, I argue that no matter how we answer this question, expected utility theory cannot provide the reason why a moral disposition like constrained maximization is to be preferred to its rivals.