The structures of LT-LiCoO2 (synthesised by reaction of Li2CO3 and CoCO3 at 400-degrees-C) and its delithiated product LT-Li0.4CoO2 have been reinvestigated by neutron powder diffraction. Despite an unusually close similarity between diffraction profiles that makes it difficult to determine whether the structures are layered or spinel-like, the data confirm that the preferred structure of the LT-LiCoO2 sample made for this study is one that has a cobalt distribution which is intermediate between an ideal layered and an ideal lithiated spinel structure. On the other hand, refinement of the data of LT-Li0.4CoO2 prepared by reacting LT-LiCoO2 with acid shows, unequivocally, that a spinel-type structure is formed. These structures are discussed in relation to previously reported electrochemical data obtained from Li/LT-LiCoO2 cells.