Three samples of YBa2 (Cuo.9oCoo.to)307_~ were prepared by different heat treatments and studied by both neutron-and highresolution X-ray diffraction. Standard samples, prepared using sintering temperatures up to 950°C in flowing oxygen, were superconducting with a midpoint near 30 K. About 0.75 formular unit of oxygen was removed by heating in flowing argon near 830°C, producing a non-superconducting reduced material. Reoxidized samples were prepared by heating the latter in flowing oxygen near 400°C. These regained the lost oxygen, but are not superconducting above 5 K. High-resolution synchrotron X-ray diffraction demonstrated the tetragonal structures of the standard and reduced specimens, as well as the orthorhombic structure of the reoxidized material. Portions of each sample were used for neutron powder diffraction studies, and the data were analyzed with the Rietveld technique. Structural parameters, including the Co occupancies on the two copper sites, were refined. The results are evaluated with respect to other neutron-diffraction, X-ray absorption fine structure, and M/Sssbauer data. The implications of these results in terms of a physical basis for the shift from tetragonal to orthorhombic symmetry are explored. We feel that oxygen reordering in the chain layers is the underlying reason for the lowering of the crystal symmetry.