A recent resurgence in logical-rule theories of categorization has motivated the development of a class of models that predict not only choice probabilities but also categorization response times (RTs; Fific, Little, & Nosofsky, 2010). The new models combine mental-architecture and random-walk approaches within an integrated framework and predict detailed RT-distribution data at the level of individual participants and individual stimuli. To date, however, tests of the models have been limited to validation tests in which participants were provided with explicit instructions to adopt particular processing strategies for implementing the rules. In the present research, we test conditions in which categories are learned via induction over training exemplars and in which participants are free to adopt whatever classification strategy they choose. In addition, we explore how variations in stimulus formats, involving either spatially separated or overlapping dimensions, influence processing modes in rule-based classification tasks. In conditions involving spatially separated dimensions, strong evidence is obtained for application of logical-rule strategies operating in a serial-self-terminating processing mode. In conditions involving spatially overlapping dimensions, preliminary evidence is obtained that a mixture of serial and parallel processing underlies the application of rule-based classification strategies. The logical-rule models fare considerably better than major extant alternative models in accounting for the categorization RTs. (Contains 11 figures, 8 tables and 7 footnotes.)