An electron diffraction and microscopy study is presented of a variety of phases in the Y:Ba:Cu:O system in which superconductivity occurs. The superconducting phase is demonstrated by convergent beam electron diffraction to be centrosymmetric with space group Pmmm, in contrast to a previous determination of Pmm2. This discrepancy arises from local symmetry‐breaking defects. In addition to this phase and a cubic BaCuO2 phase, we characterize two other phases. One is the Y‐rich orthorhombic phase: Pnma with a=13.5 Å, b=6.3 Å, and c=7.6 Å. The second occurs by a phase transition of the superconducting Pmmm phase to P4/mmm with a=3.85 Å, c=11.7 Å. The superconducting phase may now be described as either an ordered array of oxygen vacancies in the perovskite structure, or an ordered array of oxygen interstitials in the new tetragonal phase, which may explain how the material can lose oxygen reversibly.