Abstract: A discussion of the difficulties of prototype theories for describing compositional meaning motivates three experiments that inquire how well-defined concepts fare under paradigms that are commonly interpreted to support the prototype view. The stimulus materials include exemplars of prototype categories (sport, vehicle, fruit, vegetable) previously studied by others, and also exemplars of supposedly well-defined categories (odd number, even number, female, and plane geometry figure). Experiment I, using these materials, replicated the exemplar rating experiment of Rosch (1973). It showed that both the well-defined and prototypic categories yield graded responses, the supposed hall-mark of a family resemblance structure. Experiment II, using the same sorts of stimulus materials, replicated a verification-time paradigm, also from Rosch (1973). Again, the finding was that both well-defined and prototypic categories yielded results previously interpreted to support a family-resemblance description of those categories, with faster verification times for prototypical exemplars of each category. In Experiment III, new subjects were asked outright whether membership in the category of fruit, odd number, etc., is a matter of degree, or is not, and then these subjects were rerun in the Experiment I paradigm. Though subjects judged odd number, etc., to be well-defined, they provided graded responses to all categories once again. These findings highlight interpretive difficulties for the experimental literature on this topic. Part I of the discussion first outlines a dual theory of concepts and their identification procedures that seems to organize these outcomes. But Part II of the discussion argues that feature theories are too impoverished to describe mental categories, in general.