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The standard formulations of the supervenience relation present the supervenience of one set of properties on another in terms of property correlations, without placing any constraints on the dependency relation concerned. This does not ensure that properties supervening upon phys-icalistically acceptable base properties are not themselves emergent in a way at odds with materialism. So physicalism needs ‘superdupervenience’. I argue that, where supervenient and base properties are instantiated in the same individuals, Horgan’s requirement of robust explanation is neither sufficient nor necessary for superdupervenience. His paradigm case is compatible with the supervenient property‘s being emergent. This and other unacceptable possibilities may be ruled out by means of a metaphysical constraint on the supervenience relation, which must be internal. Each individual causal power in the set associated with a given supervenient property must be numerically identical with a causal power in the set associated with its base property. Satisfying this condition is all that is needed to render supervenience superduper. In fact a wide variety of non-reductive physicalist accounts are implicitly or explicitly designed to meet this condition, and so are more similar than they seem.