It is widely accepted that conscious experience has a physical basis. That is, the properties of experience (phenomenal properties, or qualia) systematically depend on physical properties according to some lawful relation. There are two key questions about this relation. The first concerns the strength of the laws: are they logically or metaphysically necessary, so that consciousness is nothing "over and above" the underlying physical process, or are they merely contingent laws like the law of gravity? This question about the strength of the psychophysical link is the basis for debates over physicalism and property dualism. The second question concerns the shape of the laws: precisely how do phenomenal properties depend on physical properties? What sort of physical properties enter into the laws' antecedents, for instance; consequently, what sort of physical systems can give rise to conscious experience? It is this second question that I address in this paper.