Single crystals of ZrO₂-15 mol % CaO and ZrO₂-9 mol % Y₂O₃, annealed for either 400 h at 1273 K or 2.5 h at 1673 K and then quenched, were examined by electron diffraction and dark-field transmission electron microscopy. The thermal treatments duplicated those of Faber, Mueller & Cooper [Phys. Rev. B (1978), 17, 4884-4888], who used elastic neutron scattering to investigate fluorite-forbidden reflections which arise from what previous authors have called the `ordered' structure. The present results show that the extra reflections are due to precipitation of tetragonal ZrO₂ in both systems. Imaging with the diffuse-scattered intensity also present reveals small domains, presumably associated with oxygen-vacancy ordering, in the cubic solid-solution matrix. The diffuse intensity is observed whether or not tetragonal ZrO₂ precipitates are present.