The paper examines an old debate concerning the correct analysis of non-constituent conjuncts in sentences like John gave [the books to Mary] and [the records to Sue]. Five possible analyses of such coordinate structures are briefly reviewed: the large conjunct, the right-branching, the gapping, the constituent conjuncts, and the non-constituent conjuncts approaches. It is argued that the latter, i.e. in terms of non-constituent conjuncts, is the best to account for the differences between conjunct-internal and conjunct-external sharing. Subject-verb agreement data demonstrate that conjunct-external shared material obeys the limitation of strict phonological identity across the conjuncts, whereas conjunct-internal shared material behaves leniently in this regard. The conclusion reached is significant. Coordination is no longer in any way a valid diagnostic for constituent structure.