The recognition that human minds/brains are finite systems with limited resources for computation has led some researchers to advance the "Tractable Cognition thesis": Human cognitive capacities are constrained by computational tractability. This thesis, if true, serves cognitive psychology by constraining the space of computational-level theories of cognition. To utilize this constraint, a precise and workable definition of "computational tractability" is needed. Following computer science tradition, many cognitive scientists and psychologists define computational tractability as polynomial-time computability, leading to the P-Cognition thesis. This article explains how and why the "P-Cognition thesis" may be overly restrictive, risking the exclusion of veridical computational-level theories from scientific investigation. An argument is made to replace the P-Cognition thesis by the "FPT-Cognition thesis" as an alternative formalization of the Tractable Cognition thesis (here, FPT stands for fixed-parameter tractable). Possible objections to the Tractable Cognition thesis, and its proposed formalization, are discussed, and existing misconceptions are clarified. (Contains 12 figures, 3 tables and 12 notes.)