In this article, we derive a nonparametric prediction from decision-bound theory (DBT). The crucial aspect that is tested is whether or not familiarity of a stimulus affects response time in categorization. We show that, for our design, DBT, extended with some reasonable and testable assumptions, predicts no familiarity effect. Our prediction is nonparametric in that, rather than fit a specific instantiation of general DBT, we posit only some general assumptions of this theory and derive the prediction from these assumptions. It is found that familiarity did have a strong impact on response time for at least half of our participants. We suggest that DBT is in itself incomplete and should be extended to account for the full range of available data.