<p>Part of the unfinished agenda of the semantic project Kripke develops in <i>Naming and Necessity</i> is the definition of rigid designation for natural-kind terms. Since the original definition was formulated for proper names, which typically designate a unique object, it is unclear how to extend it to natural kind terms. These are usually interpreted as predicative in nature and therefore as having different extensions at different possible worlds. This poses a problem for extending rigidity to predicates: By defining rigidity as sameness of extension at every possible world, most natural kind predicates turn out non-rigid. This text presents two objections to a family of theories of rigidity that attempt to define rigidity for natural kind terms based on the notion of an essentialist predicate. My argument against the view holds that two controversies make it unfit as an extension of rigidity. First, it cannot satisfy the modal desideratum unless one assumes that natural kind terms designate non-actual objects, a claim that, I argue, defenders of the view have not established. Second, it cannot be extended to certain relevant non-descriptive predicates, such as adjectival natural kind terms. I take these objections as grounds for rejecting the view.</p>