High-Tc Cu oxides such as YBa2Cu3O7 and the Bi-Sr-Ca-Cu-O systems are characterized by a near-zero oxygen-isotope effect. Recent results by Crawford et al. show, however, that the isotope effect in the La2-xSrxCuO4 system depends strongly on the doping level (x) and can significantly exceed the BCS limit. Within the framework of the BCS phonon-mediated pairing, a logarithmic (2D) Van Hove singularity in the density of states can provide a basis for understanding these anomalous isotope effects and possibly the origin of high-temperature superconductivity. © 1990 The American Physical Society.