Prioritarianism is the moral view that a fixed improvement in someone's well-being matters more the worse off they are. Its supporters argue that it best captures our intuitions about unequal distributions of well-being. I show that prioritarianism sometimes recommends acts that will make things more unequal while simultaneously lowering the total well-being and making things worse for everyone ex ante. Intuitively, there is little to recommend such acts and I take this to be a serious counterexample for prioritarianism.