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.