Nominalism in all of its manifestations, from Abelard to Quine, grows out of ontological scruples. For William Ockham and his followers in the fourteenth century, nominalism was centrally concerned with a more parsimonious treatment of the ten Aristotelian categories of being. But when it came to the alethic modalities of possibility and necessity, the nominalist program suddenly turns expansive, or so it has seemed to recent commentators, who have found in the nominalists a commitment to vast realms of purely possible beings,  and even to a possible-worlds semantics for modality. Here I argue that, quite contrary to how the nominalists are generally read, they take particular care to avoid an ontological commitment to possibilia. Indeed, although their broader semantic views make it quite natural for them to analyze modal sentences in terms of possible worlds, they deliberately eschew this way of proceeding, even at the cost of foregoing the explanatory power that their semantic theories have in other domains.