The thermal desorption characteristics of 16 astrophysically relevant species from laboratory analogues of the icy mantles on interstellar dust grains have been surveyed in an extensive set of preliminary temperature programmed desorption experiments. The species can be separated into three categories based on behaviour. Water-like species have a single relevant desorption coincident with water. CO-like species show the volcano desorption and co-desorption of trapped molecules, monolayer desorption from the surface of water ice, and multilayer desorption if initially present in sufficient abundance in an outer layer separated from the water ice. Intermediate species show the two desorptions of trapped molecules, and may show a small monolayer desorption for molecules small enough to have a limited ability to diffuse through the structure of porous amorphous water ice. Methods by which the results obtained under laboratory conditions can be adapted for astrophysical situations are discussed.