We demonstrate systematic studies of the optimization of the superconducting transition temperature in (Pb0.7Cu0.3)Sr2(Ca0.5Y0.5)Cu2O7+δ by annealing in an oxygen atmosphere. As-sintered samples with a superconducting midpoint transition temperature, Tc(midpoint), of 18 K were prepared by solid state reaction at 1000°C for 1 hr in oxygen and then quenched in air. Subsequently, the samples were annealed in the temperature range between 700 and 1000°C for 12 hr in oxygen and then rapidly quenched in air. The ultimate Tc(midpoint) increased from 30 to 48 K with an increase in the annealing temperatures from 700 to 800°C, but a further increase in the annealing temperature of the samples from 800 to 1000°C resulted in a decrease in Tc(midpoint). Based on our studies, we believe that the optimum Tc(midpoint) of 48 K arises from the removal of excess oxygen in the insulating slabs of (Pb,Cu)O in (Pb0.7Cu0.3)Sr2 (Ca0.5Y0.5)Cu2O7+δ and this leads the material to approach an optimum hole concentration. © 1992 Academic Press, Inc.