Jaegwon Kim’s causal exclusion argument says that if all physical effects have sufficient physical causes, and no physical effects are caused twice over by distinct physical and mental causes, there cannot be any irreducible mental causes. In addition, Kim has argued that the nonreductive physicalist must give up completeness, and embrace the possibility of downward causation. This paper argues first that this extra argument relies on a principle of property individuation, which the nonreductive physicalist need not accept, and second that once we get clear on overdetermination, there is a way to reject the exclusion principle upon which the causal exclusion argument depends, but third that this should not lead to the belief that mental causation is easily accounted for in terms of counterfactual dependencies.