Powder neutron diffraction has been used to determine accurate oxygen positions in five simple ternary copper(II) oxides, SrCuO, SrCuO, BiCuO, CaCuO, and LiCuO. These materials have structures based on corner- or edge-sharing CuO square planes with CuO distances between 1.907 and 2.04 Å. In KCuO the CuO square planes are distorted with two short copper oxygen bonds of 1.81 Å. The structures of the more complex materials BaCuO (x = 0, 0.07) have also been studied using powder neutron diffraction techniques and the oxygen distribution in these materials was examined. Variations in copper(II) and copper(III) geometries are interpreted in terms of bond valence calculations which have been carried out for all the materials studied.