Gundel, Hedberg and Zacharski (1993) propose a framework whereby different referring forms conventionally signal different cognitive statuses on an implica-tional ‘givenness hierarchy’. Interaction of the hierarchy with Grice’s Maxim of Quantity gives rise to scalar implicatures which further constrain the choice among forms and their interpretations when necessary conditions for more than one form are met. Wilson (1992) and Matsui (1995) show that reference assignment for NPs introduced by the definite article is constrained within Relevance Theory by the automatic selection of an interpretation that yields adequate contextual effects for minimal processing effort. This paper proposes that an optimal account of how people understand the intended referent of an NP must appeal to both the Givenness Hierarchy and Relevance Theory. Such an account still requires the first part of the Quantity Maxim, however, either as a socially based assumption or as part of the Principle of Relevance itself.