The on-line interpretation of utterances in discourse contexts was investigated by varying the type of dependency between an utterance and its context. Listeners heard short sequences of utterances ending in incomplete fragments. The fragments varied in length and in whether their anaphoric linkage to the context (by repeated names, pronouns or zero anaphors) required inferences to be resolved. The subject's task was to name a visual continuation probe that appeared at the offset of the fragment. The differences between naming latencies to appropriate versus inappropriate probes was constant across conditions, and irrespective of whether or not inference-based processes were required to determine this preference. This was interpreted as showing that on-line speech processing is not necessarily slowed down by the use of inference to link utterances to their contexts.