According to many actualist conceptions of modality, talk about possible worlds should be reduced to talk about world stories. Intuitively, a world story is a complete description of how things could be. In this paper, I will claim that the world story approach not only suffers from the well-known, expressive problem of representing the thesis of the possible existence of non-actual objects, but it has troubles in representing, in an actualistically acceptable way, the apparently more tractable thesis of the possible non-existence of actual objects. To solve this problem, I will propose a refinement of the approach by the introduction of a novel notion of maximality, local maximality.