The adsorption of an ion or a molecule onto (1 1 1) and (1 0 0) surfaces is studied by means of Monte Carlo simulations. Different models for the repulsive lateral interactions are considered. Special attention is paid to ordered overlayers, how their formation depends on the lateral interactions, and how this is manifested in the isotherm and the adlayer compressibility. The latter quantity is proportional to the current in an electrochemical voltammetry experiment, and the phase transition by which ordered overlayers are formed often gives rise a very typical sharply peaked response known as a "butterfly". We show that the shape of the butterfly depends primarily on the details of the interactions and not on the structural order of the overlayer formed. We also illustrate how certain overlayers may fail to exhibit long-range ordering due to special domain wall-type defects that freeze mismatching configurations.