The ‘completeness of physics’ is the key premise in the causal argument for physicalism. Standard formulations of it fail to rule out emergent downwards causation. I argue that it must do this if it is to feature in a valid causal argument for physicalism. Drawing on the notion of conferring causal power, I formulate a suitable principle, ‘strong completeness’. I investigate the metaphysical implications of distinguishing this principle from emergent downwards causation, and I argue that categoricalist accounts of properties are better equipped to sustain the distinction than dispositional essentialist accounts. Finally, I argue that the additional evidence needed for strong completeness renders the causal argument otiose for any properties amenable to scientific reduction.