High-pressure (3 kbar) oxygenation of (La, Sm, Sr)2CuO4 compounds having the T* structure leads to bulk superconducting transitions above 30 K and the appearance of a diamagnetic response at temperatures as high as 1/437 K. With increasing oxygenation pressure, the electrical resistivity and thermoelectric power progress from hoppinglike to more nearly metalliclike transport. The similarity in Tc and transport character with those of T-phase La2-xSrxCuO4, despite significant structural differences, further constrains possible mechanisms for superconductivity in the cuprates. © 1989 The American Physical Society.