This paper compares the performance of autistic and neurotypical participants in discourse-completion tasks that require the identification of two types of particularised conversational implicature. Material implicatures are those in which the inferential relationship from what is said to the implicature can be reconstructed without recourse to descriptions of the speaker's behaviour and the reasons underlying it, while behavioural implicatures do require such descriptions. We hypothesised that autistic participants would perform on a par with neurotypical participants in the material cases, but less well than neurotypicals in the behavioural cases, given that the latter make greater demands on theory of mind. In fact, we found that autistic participants' performance mirrored that of neurotypicals in both conditions. We note a general tendency in the literature for autistic individuals to perform well on tests of comprehending implicit communication, in contrast to attested and self-reported difficulties in this area. We speculate that this mismatch might be explained in terms of a difference in underlying competence and the performance demands of real-world interactions.