Natural-kind essentialism faces an important but neglected difficulty: the problem of complex essences (PCE). This is the question of how to account for the unity of an instantiated kind-essence when that essence consists of multiple distinct properties, some of which lack an inherent necessary connection between them. My central goal here is to propose an essentialism-friendly solution to this problem. Along the way I also employ some points from that solution to argue for the necessary truth of essentialism (necessary, that (...) is, in all possible worlds in which there are material objects), and to support the essentialist ontology of laws over and against a major rival. (shrink)