A primary criterion on which models of cognition are evaluated is their ability to fit empirical data. To understand the reason why a model yields a good or poor fit, it is necessary to determine the data-fitting potential (i.e., flexibility) of the model. In the first part of this article, methods for comparing models and studying their flexibility are reviewed, with a focus on parameter space partitioning (PSP), a general-purpose method for analyzing and comparing all classes of cognitive models. PSP is then demonstrated in the second part of the article in which two connectionist models of speech perception (TRACE and ARTphone) are compared to learn how design differences affect model flexibility. (Contains 1 table, 4 figures and 2 notes.)