Cognitive archaeologists attempt to infer the cognitive and cultural features of past hominins and their societies from the material record. This task faces the problem of _minimum necessary competence_: as the most sophisticated thinking of ancient hominins may have been in domains that leave no archaeological signature, it is safest to assume that tool production and use reflects only the lower boundary of cognitive capacities. Cognitive archaeology involves selecting a model from the cognitive sciences and then assessing some aspect of (...) the material record through that lens. We give examples to show that background theoretical commitments in cognitive science that inform those models lead to different minimum necessary competence results. This raises an important question: what principles should guide us in selecting a model from the cognitive sciences? We outline two complementary responses to this question. The first involves using _independent_ lines of evidence to converge on a particular capacity. This can then influence model choice. The second is a broader suggestion. Theoretical diversity is a good thing in science, but is only beneficial over a limited amount of time. According to recent modelling work, one way of limiting diversity is to introduce extreme priors. We argue that having a broad spectrum of views in the philosophy of cognitive science may actually help cognitive archaeologists address the problem of minimum necessary competence. (shrink)