This article examines decision processes in the perception and categorization of stimuli constructed from one or more components. First, a general perceptual theory is used to formally characterize large classes of existing decision models according to the type of decision boundary they predict in a multidimensional perceptual space. A new experimental paradigm is developed that makes it possible to accurately estimate a subject's decision boundary in a categorization task. Three experiments using this paradigm are reported. Three conclusions stand out: (a) Subjects adopted deterministic decision rules, that is, for a given location in the perceptual space, most subjects always gave the same response; (b) subjects used decision rules that were nearly optimal; and (c) the only constraint on the type of decision bound that subjects used was the amount of cognitive capacity it required to implement. Subjects were not constrained to make independent decisions on each component or to attend to the distance to each prototype.