It is often thought that a notion of general term rigidity could help explain the particular behavior of natural kind terms in modal contexts. An influential strategy for developing a non-trivial account of general term rigidity appeals to essential properties of the things to which such terms apply. I show that essentialism cannot underpin a notion of rigidity that can play the expected explanatory roles. Essentialists are committed to presuppositions that themselves play those roles without implying essentialism.