The effect of oxygen content and thermal treatment has been studied in the (Y 0.8Ca 0.2)Ba 2Cu 3O y system. The introduction of Ca altered the normal state and superconducting properties substantially. Particularly intriguing is that Ca-doped samples with more oxygen-vacancy disorder have higher superconducting transition temperatures ( T c) and lower resistivities, contrary to the non-Ca-doped system. The correlation between T c and carrier concentration cannot be described by the empirical relation observed in many high- T c oxides.