Mechanistic explanation has an impressive track record of advancing our understanding of complex, hierarchically organized physical systems, particularly biological and neural systems. But not every complex system can be understood mechanistically. Psychological capacities are often understood by providing cognitive models of the systems that underlie them. I argue that these models, while superficially similar to mechanistic models, in fact have a substantially more complex relation to the real underlying system. They are typically constructed using a range of techniques for abstracting the functional properties of the system, which may not coincide with its mechanistic organization. I describe these techniques and show that despite being non-mechanistic, these cognitive models can satisfy the normative constraints on good explanations.