Fine (1994) is widely thought to have refuted the simple modal account of essence, which takes the essential properties of a thing to be those it cannot exist without exemplifying. Yet a number of philosophers have suggested resuscitating the simple modal account by appealing to distinctions akin to the one Lewis (1983; 1986) draws between sparse and abundant properties, treating only those in the former class as candidates for essentiality. I argue that `sparse modalism' about essence succumbs to counterexamples similar to those originally posed by Fine, and fails to capture paradigmatic instances of essence involving abundant properties and relations.