Room temperature deposition of Ag on InSb(111) is known to lead to three-dimensional clustering, without long-range crystalline order. We show by means of angle-resolved photoemission that 'two-step' growth in which the films are annealed to room temperature after low temperature deposition results in the formation of Ag films which are epitaxial, atomically flat, and display a quasi-discrete quantum well band structure. Core level analysis highlights different chemical interactions between the substrate and deposited materials for room temperature and 'two-step' Ag growth.