Intensional verbs like want select for clausal complements expressing propositions, though they can be perfectly natural when combined with a direct object. There are two interesting phenomena associated with intensional transitive expressions. First, it has been suggested that their interpretation requires enriched compositional operations, similarly to expressions like began the book (e.g., Pustejovsky, 1995). Secondly, when the object position is filled by an indefinite NP, it preferentially receives an unspecific reading, under which definite anaphora is not supported (e.g., Moltmann, 1997). We report three eye-tracking experiments investigating the time-course of processing of sentence pairs like John wanted a beer. The beer was warm. Consistent with the enriched composition hypothesis, results showed that intensional transitive constructions (e.g., wanted a beer) take longer to process than control expressions (e.g., drank/wanted to drink a beer). However, contrary to previous findings, the processing of the continuation sentence appears to be not affected by whether the definite NP (the beer) can be interpreted as coreferential with the indefinite or not. We interpret the results with respect to accounts of semantic processing relying on the notions of enriched composition and non-actuality implicature