In this chapter, we explore the possible criteria for evaluating the adequacy of candidate accounts of concrete digital computation. According to proponents of CTM, cognition is computational. Before we can judge the plausibility of any particular CTM, we need to understand what notion of computation this theory employs. Although there are extant accounts of computation, any of which may, in principle, serve as a basis for CTM, it is not clear that they are all equivalent or even adequate as accounts of computation proper. By proposing a plausible alternative to Smith’s adequacy criteria, our goal here is to resist his discouraging claim that noadequate account of computation proper is possible.