Language is widely assumed to be a well designed tool for reliably communicating propositional information between people. This suggests that its users should be sensitive to failures of communication, such as utterances that are blatantly incoherent with respect to an ongoing conversation. We present experimental work suggesting that, in fact, people are surprisingly tolerant of conversational incoherence. In two previous studies, participants engaged in instant-messaging conversations that were either repeatedly crossed with other conversations or had lines inserted into them that deliberately contradicted available information. In both cases, a substantial proportion of participants failed to notice. In a new study, confederates inserted unexpected, nonsensical lines into face-to-face conversations. The majority of participants failed to notice. We argue these findings suggest that we should be wary of modeling spontaneous communication in terms of faithful information transmission, or language as a well designed tool for that purpose.