Abstract. The accessibility constraints imposed on anaphora by dynamic theories of discourse are too strong because they rule out many perfectly felicitous cases. Several attempts have been made by previous authors to rectify this situation using various tactics. This paper proposes a more viable approach that involves replacing Heim’s notion of familiarity with a generalized variant due to Roberts. This approach is formalized in hyperintensional dynamic semantics, and a fragment is laid out that successfully deals with some problematic examples