We seek to determine whether the shielding observed in the electron free-fall experiment could be performed by electrons in a surface layer. An idealized model is used to estimate the shielding of the uniform electric field produced by the gravitational compression of the ionic lattice. We allow for the possibility that the charges in the surface layer can obey either Fermi or Bose statistics. Neither a two-dimensional Fermi gas nor a two-dimensional lattice of electrons provides sufficient shielding at low temperature. A condensed Bose film could account for the magnitude of the shielding at low temperatures, although the predicted condensation temperature is considerably lower than the transition temperature observed in the experiment. Either a nondegenerate Bose film or a two-dimensional Fermi gas could account for the field observed above the transition temperature. The shielding of the patch effect field due to contact potential differences on the inner surface of the copper tube is shown to be comparable to that of the lattice compression field. The electric field produced by an axial current in the copper tube is not shielded if the surface electrons are in local equilibrium with the metallic substrate.