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Heterogeneous Fenton dominated by ·OH is limited in its application, as pre-acidification is required to maximize the generation amount and redox potential of ·OH. It is thus featured to consume resources and generate pollutants. In this study, both CuS/H 2 O 2 and Cu 2 S/H 2 O 2 are found to show better performances under close-to-neutral condition (pH 5.0 to 9.0) than acidic condition (pH 3.0) when degrading a model contaminant, sulfamethazine (SMZ), because ·OH does not play a major role in both systems. The Cu valence-dependent catalytic mechanisms are responsible for the varied kinetics between CuS/H 2 O 2 and Cu 2 S/H 2 O 2. In CuS/H 2 O 2 , Cu(III) and 1O 2 contribute to the SMZ degradation, and their contributions are pH-dependent. In Cu 2 S/H 2 O 2 , Cu(III) is responsible for the degradation regardless of the pH. Both systems with optimal performances under neutral condition are advantageous as pre-acidification can be avoided. In addition, air sparging induces additional 16% SMZ degradation in Cu 2 S/H 2 O 2 under acidic condition, because the sparged O 2 reacts with dissolved Cu(I). The more O 2 reacts with the dissolved Cu(I), the less generated Cu(III) is ineffectively depleted. Air sparging is readily applicable to different operations, thus its combination with Cu 2 S/H 2 O 2 potentially benefits the development of environmentally-friendly treatment process for industrial wastewater. • CuS/H 2 O 2 and Cu 2 S/H 2 O 2 are more effective under neutral than acidic condition. • Cu(III) is critical in Cu 2 S/H 2 O 2 , independent of solution pH. • Cu(III) and 1O 2 are critical in CuS/H 2 O 2 , but pH dependent. • Air sparging is an cleaner alternative to improve the Cu 2 S/H 2 O 2 performance. [ABSTRACT FROM AUTHOR]