 Not all identity statements widely accepted as necessary specify a theoretically interesting essence in the relevant respect. ‘Hesperus = Phosphorus’ or ‘Cicero = Tully’ do not; each sentence contains only names for an object. But take, on the other hand, ‘Cicero = the organism descended from sperm s and egg e’, where ‘s’ and ‘e’ are names for the right sperm and egg. Many regard this sentence as necessarily true and revealing of a theoretical essence of Cicero: roughly, a theoretically interesting property possessed by Cicero in all possible worlds and never possessed by anyone else (bear in mind, for this example, limited demands of weak necessity).  In order for any identity statement to be true of necessity, both designators must be rigid if either is. And if ‘the organism descended from sperm s and egg e’ indeed expresses an essence of Cicero, it must designate just Cicero in all possible worlds, and hence rigidly: so, given that the statement at issue is necessarily true, ‘Cicero’ must be rigid, too. Alternatively, if ‘Cicero’ is rigid, as is widely acknowledged, then in order for the statement at issue to be necessarily true, ‘the organism descended from sperm s and egg e’ must be rigid and so express an essence of Cicero.