Abstract: I offer a novel objection to Jaegwon Kim's Supervenience Argument. I argue that the Supervenience Argument relies upon an untenable conception of the base physical properties upon which mental properties are supposed to supervene: the base properties are required to be both ordinary physical/causal properties and also unconditionally sufficient for the properties that they subvene. But these requirements are mutually exclusive; as a result, at least two premises in the Supervenience Argument are false. I argue that this has disruptive consequences both for the reductive position that Kim defends and the non-reductive position that he attacks. Neither side in the debate over the status of functionally conceived mental properties comes out unscathed.