It has become evident that mind–body supervenience, as merely specifying a covariance between mental and physical properties, is consistent with clearly non-physicalist views of the mental, such as emergentism. Consequently, there is a push in the physicalist camp for an ontologically more robust supervenience, a “superdupervenience,” that ensures that properties supervening on physical properties are physicalistically acceptable. Jessica Wilson claims that supervenience is made superduper by Condition on Causal Powers (CCP): each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. Furthermore, according to Wilson, a wide variety of physicalist positions, both reductive and non-reductive, can be seen as relying on CCP to ensure that properties supervening on physical properties are physicalistically acceptable. I argue that imposing CCP on mind–body supervenience fails to ensure that mental properties are physicalistically acceptable. The problem, I contend, is that while CCP may guard against supervenient mental properties being insufficiently grounded in their physical bases it fails to guard against supervenient mental properties being too deeply grounded in their physical bases.