In this paper, we further discuss the optical properties of solid-rare-gas mixtures in the soft-x-ray region. We consider the systems Ne-Ar, Ar-Kr, and Ne-Kr. We consider only the lowest conduction band whose state density is computed in a virtual-crystal approximation including off-diagonal randomness and the lowest $n=1$ exciton position. Selected compositions are, also as a check, computed using a self-consistent single-site model including off-diagonal randomness. From this we consider the core-level absorption spectra for these crystals. The paper differs from a paper by Kunz and Mickish in that we actually calculate the alloy state density rather than infer it from the pure materials, and in that we actually calculate the exact position for the core-state band edges (this is the first such calculation for a solid rare gas) and actually calculate the position of the $n=1$ exciton line.