Sulfur and oxygen adsorbed on Cu(100) have nearly identical bonding geometries and electronic structures. But they show strikingly different trends in their scattering of conduction electrons, as reflected in the variation of the substrate's surface resistivity with adsorbate coverage. For oxygen the surface resistivity varies linearly with coverage, as expected for noninteracting adsorbates. For sulfur, however, the coverage dependence is highly nonlinear, with the resistivity increasing strongly at low coverage and then becoming nearly constant above about 0.15 ML. Measurements on sputtered surfaces show that defects and adlayer ordering are not responsible for the nonlinearity. Instead, it must be attributed to interactions between the adsorbed atoms that modify the electronic structure near the Fermi level so as to diminish each atom's scattering cross-section.