The physicalist thesis that all entities are nothing over and above physical entities is often interpreted as appealing to a supervenience-based account of "nothing over and aboveness”, where, schematically, the A-entities are nothing over and above the B-entities if the A-entities supervene on the B-entities. The main approaches to filling in this schema correspond to different ways of characterizing the modal strength, the supervenience base, or the supervenience connection at issue. I consider each approach in turn, and argue that the (...) resulting formulation of physicalism is compatible with physicalism’s best traditional rival: a naturalist emergentism. Others have argued that supervenience-based formulations of physicalism fail. My aim here, besides addressing the full spectrum of supervenience-based approaches, is to show how certain philosophical and scientific theses concerning naturalism, properties, and laws give us new reasons to think that supervenience-based formulations of physicalism are untenable. (shrink)