Levinson (1985,1987a,1991) and Ariel (1985a&b, 1987,1988a, 1990a, 1991) have each proposed to anchor discourse and sentential anaphora within a more general theory of communication. Levinson chose a general, extra-linguistic pragmatic theory. He uses Grice's Quantity maxim to account for the distribution of zeros, reflexives, pronouns and lexical NPs, claiming that coreferent readings are preferred, unless a disjoint reading is implicated (by the revised Gricean maxims he offers). I have proposed a specifically linguistic, cognitive theory, whereby speakers guide addressees’ retrievals of mental representations corresponding to all definite NPs (coreferent as well as disjoint) by signalling to them the degree of Accessibility associated with the intended mental entity in their memory. An examination of actual data reveals that Levinson's predictions regarding definite NP interpretations are often not borne out. In addition, his proposals cannot account for many anaphoric patterns actually found in natural discourse. Accessibility theory, it is argued, can account for both types of problematic data.