A model for the underpotential deposition of Cu on Au(111) in the presence of bisulfate ions has recently been proposed. In this model it was assumed that the bisulfate ions formed a square-root 3 x square-root 3 template. This template leaves a honeycomb lattice of free sites for the adsorption of copper. The clear implication is that the first peak corresponds to two-thirds of a monolayer of Cu. The second peak corresponds to the replacement of the bisulfate by copper in the adlayer. We showed also that the broad foot of the first peak is due to a second-order hard-hexagon-like transition, which has been seen experimentally. The interpretation, based on scanning tunneling microscopy and low energy electron diffraction observations, that the first peak corresponds to only one-third of a monolayer, is consistent with our model if it is the bisulfate ion that is actually seen in those experiments. In the present work we discuss further refinements of this theory. We show that, from the dimensions of the bisulfate ion, an oxygen atom protrudes 1.84 angstrom above the plane of copper adsorption and the hydrogen atom of the bisulfate protrudes 2.13 angstrom. For the same geometry on a clean Au(111) surface, the bisulfate layer should stand about 4.1 angstrom above the surface. However, scanning tunneling microscopy cannot measure absolute heights, and therefore both cases appear as a square-root 3 x square-root 3 overlayer. The dependence of the peak position on concentration is also discussed using a recently developed theory of kinetic effects.