I examine a major objection to the mechanistic view of concrete computation, stemming from an apparent tension between the abstract nature of computational explanation and the tenets of the mechanistic framework: while computational explanation is medium-independent, the mechanistic framework insists on the importance of providing some degree of structural detail about the systems target of the explanation. I show that a common reply to the objection, i.e. that mechanistic explanation of computational systems involves only weak structural constraints, is not enough to save the standard mechanistic view of computation-it trivialises the appeal to mechanism, and thus makes the account collapse into a purely functional view. I claim, however, that the objection can be put to rest once the account is appropriately amended: computational individuation is indeed functional, while mechanistic explanation plays a role in accounting for computational implementation. Since individuation and implementation are crucial elements in a satisfying account of computation in physical systems, mechanism keeps its central importance in the theory of concrete computation. Finally, I argue that my version of the mechanistic view helps to provide a convincing reply to a powerful objection against non-semantic theories of concrete computation: the argument from the multiplicity of computations.