By using a simple model, we show that the density of states of a metallic overlayer deposited on a metallic substrate contains resonances (size quantization peaks) that do not broaden as an effect of the overlayer-substrate coupling, but remain well-defined features for different values of the coupling parameter. Instead, these modes become sharper by increasing the thickness of the overlayer. We also investigate the influence of the work function on the localized and resonant states associated with the overlayer. This effect, which, in general, is not considered in tight-binding models, is most significant for the highest localized or resonant mode, which becomes a surface mode of the overlayer.