By using a very stable, high resolution scanning tunnelling microscope we have imaged the molecules CO, C2H2, C2H4 and C6H6 adsorbed at 4 K on a Cu{110} surface. By simultaneously determining the substrate corrugation and the position of the molecule under conditions of weak tip–surface interaction, it was found that CO occupies the atop site and that C2H2 is probably adsorbed in the short bridge site. For C2H2, a stable (probably chemisorbed) species could only be imaged after increasing the tunnel voltage above 1 V. Energy transfer is obviously required before the molecule ‘locks’ into the short-bridge site. As expected, C6H6 appears to adsorb with its molecular plane parallel to the surface but only an indirect determination of the adsorption site was possible. These experiments demonstrate the potential, and some of the limitations, of adsorption-site determination with the scanning tunnelling microscope.