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We present a joint study of the band offsets and exciton binding energies in Zn1-xCdxSe-ZnSe quantum wells grown by metal-organic vapor-phase epitaxy with cadmium composition ranging up to 22%. The optical-spectroscopy data presented here are the wavelength derivative of the 2-K reflectance. The strained band-gap difference is divided as follows: the heavy-hole valence-band share deduced from the calculation is 32±1%; the remainder is allotted to the electron conduction band. The exciton binding energy has been calculated within the context of two methods: first, we propose a variational calculation using an exciton wave function written as the product of the envelope-function solutions of the square-well problem with a hydrogenlike two-parameter trial function. Second, as the light-hole potential is marginally type I, we lay out a more sophisticated computation based on a self-consistent variational approach that gives both the exciton binding energies and the self-consistent light-hole densities of probability. We compare the full information given by these two approaches.