Fitting models to behavior is commonly used to infer the latent computational factors responsible for generating behavior. However, the complexity of many behaviors can handicap the interpretation of such models. Here we provide perspectives on problems that can arise when interpreting parameter fits from models that provide incomplete descriptions of behavior. We illustrate these problems by fitting commonly used and neurophysiologically motivated reinforcement-learning models to simulated behavioral data sets from learning tasks. These model fits can pass a host of standard goodness-of-fit tests and other model-selection diagnostics even when the models do not provide a complete description of the behavioral data. We show that such incomplete models can be misleading by yielding biased estimates of the parameters explicitly included in the models. This problem is particularly pernicious when the neglected factors are unknown and therefore not easily identified by model comparisons and similar methods. An obvious conclusion is that a parsimonious description of behavioral data does not necessarily imply an accurate description of the underlying computations. Moreover, general goodness-of-fit measures are not a strong basis to support claims that a particular model can provide a generalized understanding of the computations that govern behavior. To help overcome these challenges, we advocate the design of tasks that provide direct reports of the computational variables of interest. Such direct reports complement model-fitting approaches by providing a more complete, albeit possibly more task-specific, representation of the factors that drive behavior. Computational models then provide a means to connect such task-specific results to a more general algorithmic understanding of the brain.