In English coordinate ellipsis constructions, the determinerof a DP in the second conjunct can sometimes be omitted under identity with the determiner of the corresponding constituent of the first conjunct, a phenomenon known as 'determiner sharing'. Following Williams's (1997) analysis of nonconstituent ellipsis, we argue that determiner sharing involves a two-step elision process: coordinate ellipsis plus a process we term 'dependent ellipsis'. Dependent ellipsis is the process by which a coordinate null head licenses the heads of its direct dependents to be null as well. We show that, under the hypothesis that dependent ellipsis is not a transitive relation, the properties of determiner sharing constructions follow, adding some new observations to those noted before in the literature. For example, we explain that subject determiner sharing is usually only possible if Tense is gapped in the second conjunct while object determiner sharing is dependent on Verb-gapping. However, we also show that in certain cases subject D-sharing may be possible without T-gapping, and, vice versa, there are cases where T-gapping does not license subject D-sharing.