The paper takes into account some aspects of Element Theory, a segmental theory developed in the framework of Government Phonology. The focus is on some revisions of classical Element Theory concerning the elemental inventory and the notion of headedness: on the one hand these models propose that the element set should be very small, while on the other hand they allow for a looser conception of headedness and dependency relations. It is here observed that a generalised concern about overgeneration influences, in an unduly way, the criteria for defining the element set, attributing priority to economy over cognitive adequacy in segmental representations. The paper proposes that the original purpose of Element Theoryof modelling phonological competence should be maintained.