High-transition-temperature superconductivity arises in copper oxides when holes or electrons are doped into the CuO2 planes of their insulating parent compounds. Whereas hole doping quickly induces metallic behaviour and superconductivity in many cuprates, electron doping alone is insuffcient in materials such as R2CuO4 (R is Nd, Pr, La, Ce and so on), where it is necessary to anneal an as grown sample in a low-oxygen environment to remove a tiny amount of oxygen in order to induce superconductivity. Here we show that the microscopic process of oxygen reduction repairs Cu deficiencies in the as-grown materials and creates oxygen vacancies in the stoichiometric CuO2 planes, effectively reducing disorder and providing itinerant carriers for superconductivity. The resolution of this long-standing materials issue suggests that the fundamental mechanism for superconductivity is the same for electron- and hole-doped copper oxides.