According to many, that the normative supervenes on the non-normative is a truism of normative discourse. This chapter argues that those committed to more specific moral, aesthetic, and epistemic supervenience theses should also hold (NS*): As a matter of conceptual necessity, whenever something has a normative property, it has a base property or collection of base properties that metaphysically necessitates the normative one. The main aim in this chapter is to show that none of the available arguments establish (NS*), or indeed the relevant epistemic, aesthetic, and moral supervenience theses. (NS*) is not a conceptual truth. This has considerable dialectical importance. One interesting upshot is that it affords non-reductivists and non-naturalists a novel way of resisting certain prominent supervenience-based objections to their views, including objections that formulate supervenience as a purely metaphysical thesis.