 Several philosophers have argued that rigid designation for kind and other general terms faces a serious objection: rigid designation for kind terms is trivial (Soames 2002; Schwartz 2002; Martí 2004). Rigid designation requires that the object designated by a rigid designator be the same in all worlds. That requirement rules out the extension of a kind term as its designation, since the same kind may have different extensions in different worlds. On the other hand, regarding the extension as an abstract individual also faces difficulties. One might take ‘Mary’s favourite colour’ to designate different colours in different worlds, and thus understood it is not a rigid designator. But we could take ‘Mary’s favourite colour’ to designate (rigidly) an unusual abstract individual Mary’s-favourite-colour, which has violet things as its extension in the actual world, but turquoise things in another possible world and so on. This thought experiment suggests that it is always possible to regard a general term as a rigid designator. One option for resisting this move is to deny that in every case there is some entity for the term to refer to. There is no thing abstract or concrete that is Mary’s-favourite-colour. Property terms may denote a natural property, in Lewis’s (1986) terms a sparse property or they do not denote at all. Similarly, natural kind terms denote genuinely natural entities that are likewise sparse or they fail to denote.