The desorption characteristics of molecules on interstellar dust grains are important for modelling the behaviour of molecules in icy mantles and, critically, in describing the solid–gas interface. In this study, a series of laboratory experiments exploring the desorption of three small molecules from three astrophysically relevant surfaces is presented. The desorption of CO, O₂ and CO₂ at both submonolayer and multilayer coverages was investigated from non-porous water, crystalline water and silicate surfaces. Experimental data were modelled using the Polanyi–Wigner equation to produce a mathematical description of the desorption of each molecular species from each type of surface, uniquely describing both the monolayer and multilayer desorption in a single combined model. The implications of desorption behaviour over astrophysically relevant time-scales are discussed.