The present contribution starts from two well-known theoretical concepts. One is Reis’ metatheoretical idea of realistic grammar; the other is Keenan & Comrie’s Noun Phrase Accessibility Hierarchy. After introducing and discussing both concepts, I connect them by asking whether the notion of gaps in realistic grammar might include any non-accessibility of positions on the Noun Phrase Accessibility Hierarchy and on typological hierarchies more generally. As a case in point, I present a questionnaire study which confirms the usual assumption that OCOMP is not accessible for relativization in Standard German. On this basis, the general question will be answered in the negative: non-accessibility is not a gap. This answer then raises new questions, in particular: how can any non-accessibility of positions on typological hierarchies be accounted for in first language acquisition? I sketch a solution to this problem, the technical details of which are, however, left for future research.