There are two major semantic theories of proper names: Semantic Descriptivism and Direct Reference. According to Semantic Descriptivism, the semantic content of a proper name N for a speaker S is identical to the semantic content of a definite description “the F” that the speaker associates with the name. According to Direct Reference, the semantic content of a proper name is identical to its referent. Semantic Descriptivism suffers from a number of drawbacks first pointed out by Donnellan (1970) and Kripke (1972). Direct Reference faces difficulties of its own, most importantly the problem of empty names. The most promising Directly Referential solution to this problem is the Unfilled Proposition view, according to which utterances of sentences containing empty names semantically express unfilled propositions. But this view faces the problem of accounting for the intuition that negative existentials involving empty names are true. The most promising way of dealing with this problem within Unfilled Proposition theory is to suppose (i) that utterances of sentences may be used to pragmatically convey propositions they do not semantically express, and (ii) that the proposition pragmatically conveyed by a speaker S's utterance of a sentence containing an empty name N (where “the F” is a definite description S associates with N) is identical to the proposition semantically expressed by an utterance of the sentence obtained by replacing N with “the F”. Call this view “Pragmatic Descriptivism”. With respect to the problem of negative existentials, Pragmatic Descriptivists can insist that, although an utterance of “Santa does not exist” is literally neither true nor false, our taking it to be true may be explained as the result of our having confused the unfilled proposition it semantically expresses with the clearly true descriptive proposition it pragmatically conveys. Despite its theoretical virtues, Pragmatic Descriptivism has recently come under fire. Everett (2003), in particular, has advanced four different lines of criticism, to which Adams and Dietrich (2004) have responded in some detail. In this article, I have two main aims. The first is to argue that Adams and Dietrich's replies to Everett's criticisms (with one exception) are ineffective. I conclude that there is no acceptable strategy for solving the problem of empty names within Direct Reference theory. The second is to argue that there is a promising alternative to Semantic Descriptivism and Direct Reference that requires us to fill unfilled propositions with names, thereby solving the problem of empty names.