Though cognitive science has given psychology a new, more detailed and specific way of expressing models of cognition, correspondingly detailed and precise arguments analyzing and supporting those models have not been forthcoming. Consequently, the new models often fail to meet the traditional criteria of scientific theories. Tools are available or can be developed which will help cognitive scientists build computational cognitive theories that will meet some widely-accepted standards. The prime tool (or class of tools) is the competitive argument, which involves explication of the principles of a theory and its entailments, and comparison of theories to other theories and with alternative versions of itself. The evolution of one theory can be examined as it develops through a natural progression of stages, including task analysis, articulation of principles, and competitive argumentation. A 34-item reference list is included. (Author/LMM)