The phenomenon of that-deletion in English has traditionally been taken to be one of the prime examples of syntactic free variation: it has implicitly been assumed that the language arbitrarily allows predicates to embed their propositional complements with the complementizer that (as that-clauses), or without it (as bare clauses). Different researchers, however, have demonstrated that the complementizer CANNOT be deleted under certain classes of predicates. In this article, I show that the distribution of that-deletion across the different predicate classes is determined by a single semantic property, which I call "truth claim": that-deletion is possible under predicates which semantically entail that a cognitive agent (most often their subject) has made an epistemic claim concerning the truth of the proposition denoted by the embedded clause. In some cases, that-deletion is also possible under predicates which pragmatically approximate the meanings of real truth claim predicates. This pattern is explained on the basis of semantic compatibility. I suggest that that-clauses and bare clauses have different meanings: that-clauses denote propositions, but bare clauses denote what I call "asserted propositions." Only truth claim predicates, and those predicates which can be pragmatically used as such, are compatible with asserted propositions. Consequently, only they are capable of embedding bare clauses. To account for the impossibility of that-deletion in non-complement positions, the above semantic theory is supplemented with a complexity-based, adjacency-type constraint on the pronunciation of the bare clause.