This study evaluates the effect of presuppositional information associated with contrastive stress on on-line language processing. An eye-tracking methodology was used, in which eye movement latencies to real objects in a visual display are taken as a measure of on-line reference resolution. Results indicate that presupposed contrast sets are being computed on-line, and can be used to speed reference resolution by narrowing the referential domain of an utterance. In addition, presupposed contrast sets appear to play a role in managing attention in the processing of a discourse.