Superconductivity withTc&bartil;25–45 K has been induced in films based on the ‘‘infinite layer’’ structure though high temperature annealing in an oxygen ambient. The films had compositions Srn+1CunO2n+1+&dgr;(n=3–9) and were previously grown by laser molecular beam epitaxy by periodic insertion of SrO defect layers into the SrCuO2infinite layer matrix. A marked dependence on the cooling rate at the end of the postgrowth anneals indicates that preservation of a high temperature oxygen sublattice forms the key to enhancing the carrier density in these films, opposite to the situation with YBa2Cu3O7−&dgr; . ©1995 American Institute of Physics.