The mReactr system is a computational implementation of the mental model theory of reasoning (Johnson-Laird, 1983) that is embedded within the ACT-R cognitive architecture (Anderson, 1990). We show how the memory-handling mechanisms of the architecture can be leveraged to store and handle discrete representations of possibilities, i.e., mental models, efficiently. Namely, the iconic representation of a mental model can be distributed, in which each component of a model is represented by a “chunk” in ACT-R’s declarative memory. Those chunks can be merged to create minimal mental models, i.e., reduced representations that do not contain redundant information. Minimal models can then be modified and inspected rapidly. We describe three separate versions of the mReactr software that minimize models at different stages of the system’s inferential processes. Only one of the versions provides an acceptable model of data from an immediate inference task. The resulting system suggests that reasoners minimize mental models only when they initiate deliberative mental processes such as a search for alternative models.