Non-reductive moral realism is the view that there are moral properties which cannot be reduced to natural properties. If moral properties exist, it is plausible that they strongly supervene on non-moral properties- more specifically, on mental, social, and biological properties. There may also be good reasons for thinking that moral properties are irreducible. However, strong supervenience and irreducibility seem incompatible. Strong supervenience entails that there is an enormous number of modal truths (specifically, truths about exactly which non-moral properties necessitate which moral properties); and all these modal truths must be explained. If these modal truths can all be explained, then it must be a fundamental truth about the essence of each moral property that the moral property is necessarily equivalent to some property that can be specified purely in mental, social and biological terms; and this fundamental truth appears to be a reduction of the moral property in question. The best way to resist this argument is by resorting to the claim that mental and social properties are not, strictly speaking, natural properties, but are instead properties that can only be analysed in partly normative terms. Acceptance of that claim is the price of non-reductive moral realism.