The low-Reynolds-number collision and rebound of two rigid spheres moving in an ideal isothermal gas are studied in the lubrication limit. The spheres are non-Brownian in nature, with radii much larger than the mean-free path of the molecules. The nature of the flow in the gap between the particles depends on the relative magnitudes of the minimum gap thickness, the mean-free path of the bulk gas molecules, and the gap thickness at which compressibility effects become important. Both the compressible nature of the gas and the non-continuum nature of the flow in the gap are included and their effects are studied separately and in combination.