Non-actualist theories promise straightforward accounts of meaning, truth and reference of fictional discourse but are ostensibly saddled with a Selection Problem, that multiple possible candidates satisfy the role-descriptions associated with names used in fictions and no principled way to distinguish between them; yet if names are referential, there can only be one referent. The problem is often taken to be a serious—even decisive—obstacle for non-actualism, and the aim of this article is to show that the challenge can be met. I (...) suggest that storytellers and authors fix the referents of referential terms they use by arbitrary selecting referents through simple acts of stipulation, and then determine which of the worlds containing the relevant individuals serve as truth-makers for the story by adding properties to the characters. The resulting view of reference is consistent with reasonable, foundational requirements on reference, such as a causal-historical theory, and can moreover be used to support plausible theories of truth in fiction and facilitate elegant models of fiction as a type of discourse. (shrink)