In the space of possible worlds, there might be a best possible world (a uniquely best world or a world tied for best with some other worlds). Or, instead, for every possible world, there might be a better possible world. Suppose that the latter is true, i.e., that there is no best world. Many have thought that there is then an argument against the existence of God, i.e., the existence of an omnipotent, omniscient and morally perfect being; we will call such arguments no-best-world arguments. In this paper, we discuss ability-based objections to such arguments; an ability-based objection to a no-best world argument claims that the argument fails because one or more of its premises conflict with a plausible principle connecting the applicability of some type of moral evaluation to the agent’s possession of a relevant ability. In particular, we formulate and evaluate an important new ability-based objection to the most promising no-best world argument.