It has long been argued, and often admitted, that utilitarianism cannot account for distributive Justice. The purpose of this paper is to show that utilitarianism cannot make sense of the moral issues involved in having children. In particular, it cannot take account of the differences between infanticide, abortion, contraception and chastity. Importantly, the two difficulties stem from a common feature of utilitarianism, that since it is a sum-ranking decision procedure, it is structurally indifferent to who experiences utility. Children and Justice are two cases where it makes every difference how the utility total is distributed among people.