Utilitarianism seems to require us to sacrifice a person if doing so will produce a net increase in the amount of utility. This feature of utilitarianism is extremely unattractive. The puzzle is how to reject this requirement without rejecting the plausible claim that we are often wise to trade lesser amounts of utility for greater amounts. I argue that such a position is not as paradoxical as it may appear, so long as we understand the relationship between the value of utility and the value of persons in a certain way. I argue that the traditional utilitarian position assumes an inadequate view of this relationship. I suggest a more plausible view of this relationship, one which implies that we may not sacrifice a person merely in order to produce a net gain in utility, where that utility does not result from the saving of any other persons’ lives.