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Binding energies of excitons in a quantum-well structure are calculated including fully the effects of image charges, finite barriers, the z correlation of electrons and holes, and anisotropic hole masses. The influence of discontinuous masses and discontinuous dielectric constants across the interfaces is evaluated in detail: While the mass difference becomes important only when the excitonic wave function penetrates into the barrier, the image charges appreciably modify the Coulomb interaction and therefore influence the exciton binding energy even at well widths larger than the exciton Bohr radius. Results for technologically important, particular material systems are presented.The well-recognized importance of excitonic effects on the optical properties of semiconductor quantum wells (QW's) (Refs. 1-3) has attracted much attention to the calculation of exciton binding energies in these structures. ' Although the problem is well defined, theoretical calculations for realistic structures with different material parameters in the well and barrier region were carried out with several approximations up to now. In contrast, three-dimensional