This paper points out the merit of Nagelian reduction, namely to propose a model of inter-theoretic reduction that retains the scientific quality of the reduced theory and the merit of functional reduction, namely to take multiple realization into account and to offer reductive explanations. By considering Lewis and Kim’s proposal for local reductions, we establish that functional reduction fails to achieve a theory reduction and cannot retain the scientific quality of the reduced theory. We improve on that proposal by showing (...) how one can build functional sub-types that are coextensive with physical realizer types and thereby obtain a theory reduction that is explanatory and that vindicates the scientific quality of the special sciences. (shrink)