We study the adsorption of polyelectrolytes onto oppositely charged surfaces as the surface charge density is varied while keeping the polyelectrolyte charge density fixed. As observed previously from multilayer adsorption studies,(1,2) nonmonotonic adsorption behavior is obtained in the intermediate surface charge density regime, with anomalously thick "supermonolayers" transitioning to molecularly thin lavers over a small range of surface charge densities. A simple adsorption model is introduced to explain these findings, in which the surface is characterized by discrete and fully compensated adsorption sites.