The majority of cognitive models support some form of parameterization, either of the model itself, or through architectural mechanisms. In order to fully understand these models, it is important to understand the model’s behavior as a result of parameter variation across a wide range of values. Even simple models become difficult to understand without a systematic method of exploring performance across parameter combinations, and scientists have turned to iterative methods to perform sweeps of these spaces. As an alternative to an exhaustive, homogeneous search, we examined adaptive mesh refinement (AMR) to explore simple and complex parameter spaces of several models developed within ACT-R. AMR allows for fewer model runs with minimal loss of information. We found that, with appropriate granularity, AMR methods can provide a sufficient computational exploration of a performance space with only 1% of the sampling of conventional, homogeneous parameter sweeps. The advantages of AMR for computationally efficient exploration of the performance predictions should be of benefit and interest to developers and users of cognitive architectures and cognitive models.