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Results. In the underinformative trials there were 54% pragmatic responses, comparable to the implicature rates found in previous studies. We fitted a series of mixed logit models with random intercepts for subjects and items to the subset of the eye movement data on which participants were not already looking at the target at quantifier onset. Participants were faster to converge on the target for “all” than for “some” when the quantifier referred to the small set, but not when it referred to the big set. Similarly, number terms were resolved more rapidly than “some” in the subitizing range, but not otherwise. In addition, looks to the target were delayed for “some” relative to “all” when the speaker was incompetent but not otherwise. We thus found evidence for rapid computation of scalar implicatures even in the presence of number terms, as long as the interpretation of “some” occurs outside the subitizing range, replicating and extending previously established results. Additionally, we have shown that comprehenders are sensitive to the speaker’s epistemic state. A methodological consequence of these results is that it is important to either control for or explicitly model the effect of set size when using visual-world eye-tracking to study scalar implicature. Theoretically, our results show that scalar implicatures may be computed with the speed associated with default inferences if strongly supported by probabilistic constraints, but may require the processing effort associated with typical particularized conversational implicatures if constraints are weak or in competition. Thus, scalar implicatures do not fit neatly into the GCI-PCI distinction established by Grice.