The philosophical technical term "supervenience" is frequently used in the philosophy of mind as a concise way of characterizing the core idea of physicalism in a manner that is neutral with respect to debates between reductive physicalists and nonreductive physicalists. I argue against this alleged neutrality and side with reductive physicalists. I am especially interested here in debates between psychoneural reductionists and nonreductive functionalist physicalists. Central to my arguments will be considerations concerning how best to articulate the spirit of the (...) idea of supervenience. I argue for a version of supervenience, "fine-grained supervenience," which is the claim that if, at a given time, a single entity instantiates two distinct mental properties, it must do so in virtue of instantiating two distinct physical properties. I argue further that despite initial appearances to the contrary, such a construal of supervenience can be embraced only by reductive physicalists. (shrink)