Most versions of utilitarianism depend on the plausibility and coherence of some conceptionof maximizing well-being, but these conceptions have been attacked on various grounds. This paper considers two such contentions. First, it addresses the argument that because goods are plural and incommensurable, maximization is incoherent. It is shown that any conception of incommensurability strong enough to show the incoherence of maximization leads to an intolerable paradox. Several misunderstandings of what maximization requires are also addressed. Second, this paper responds to the argument that rationality is not a matter of maximizing, but of expressing proper attitudes. This ‘expressivist’ position is first explicated through the elaboration of several paradoxes. It is then shown how, through an application of economic and strategic thinking, these paradoxes can be dissolved. The paper then concludes with some reflections on the indispensability of calculation for moral and prudential reasoning.