Conversational partners expect each other to communicate rationally and cooperatively and to contribute relevant and informative utterances. Occasionally, however, speakers produce trivial utterances which may violate our expectations of informativity. These utterances can prompt listeners to draw inferences about a speaker’s goals in producing such an utterance. Here we present two studies investigating how and when listeners derive informativity-based inferences. The results demonstrate that speaker knowledge plays an important role in the computation of inferences. Furthermore, the timecourse of the results suggests that these inferences do not always arise automatically and that their computation is costly.