The interaction between monoatomic steps on a vicinal ∼ (111) copper surface and the adsorbed sulphur monolayer has been investigated by a method involving the existence of two possible structures of the monolayer. The parts of the surface occupied by each structure, which are equal on a perfect (111) crystal plane, and differ on a vicinal surface (selective effect of the steps), have been deduced from LEED intensity measurements. Experiments on a wide range of surfaces have revealed a very strong selective effect of the steps, even for misorientations as small as 4° off the (111) plane. On surfaces with 〈3 2 1〉 steps, only one monolayer structure exists, which appears to fit perfectly the steps. The behaviour of the other surfaces having the same misorientation angle allowed us to devise a model of the step/monolayer interaction, which includes a partial decomposition of a step into the two nearest 〈3 2 1〉 steps (2D “faceting”). A general framework for exploiting experiments of the kind described above, on other adsorption systems, is also outlined.