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We report the characterization of series of oxygen deficient Ba₂YCu₃O_x samples for 7 ≥ x ≥ 6 prepared by Zr gettered annealing at 440°C. Measurements include complete crystal structure analysis at 5 K by powder neutron diffraction, electron microscopy study of the oxygen ordering, and magnetic measurements of the superconducting transitions, with particular attention to the transition widths. The results show for the first time that the 90 K and 60 K plateaus in T_c as a function of oxygen stoichiometry are associated with plateaus in the effective valence of the plane coppers. We also correlate the disappearance of superconductivity for x < 6.5 with an abrupt transfer of negative charge into the CuO₂ planes. We propose that different ordering schemes of oxygen have different characteristic T_c's between 90 and 60 K.