Supervenience has provided a way for nonreductive materialists to explain how the mental can be physically irreducible but still physically respectable. In recent years, doubts about this research program have emerged from a number of quarters. Consequently, Terence Horgan has argued that nonreductive materialists must appeal to an upgraded "superdupervenience," if supervenience is to do any materialist work. We argue that nonreductive materialism cannot meet this challenge. Superdupervenience is impossible.