This paper discusses the relevance of models for cognitive science that integrate mechanistic and computational aspects. Its main hypothesis is that a model of a cognitive system is satisfactory and explanatory to the extent that it bridges phenomena at multiple mechanistic levels, such that at least several of these mechanistic levels are shown to implement computational processes. The relevant parts of the computation must be mapped onto distinguishable entities and activities of the mechanism. The ideal is contrasted with two other (...) accounts of modeling in cognitive science. The first has been presented by David Marr in combination with a distinction of “levels of computation”. The second builds on a hierarchy of “mechanistic levels” in the sense of Carl Craver. It is argued that neither of the two accounts secures satisfactory explanations of cognitive systems. The mechanistic-computational ideal can be thought of as resulting from a fusion of Marr’s and Craver’s ideals. It is defended as adequate and plausible in light of scientific practice, and certain metaphysical background assumptions are discussed. (shrink)