Abstract Existential rules generalize Datalog with existential quantification in the head. Natively, Datalog is interpreted under a closed-world semantics, while existential rules typically employ the open-world assumption. The interpretation domain in the latter case is enlarged by infinitely many “anonymous” individuals. Then, in any rule, each variable ranges over all individuals, even if not needed or required. In this paper, we enhance existential rules by closed-world variables to consciously reason on the properties of “known” (non-anonymous) and arbitrary individuals in different ways. Accordingly, we uniformly generalize the basic classes of existential rules that ensure decidability of ontologybased query answering. For them, after observing that decidability is preserved, we prove that a strict increase in expressiveness is gained, and in most cases the computational complexity is not altered.