The electronic structure of three surface or near-surface states on stepped Cu͑775͒ has been investigated using angle-resolved, resonant, two-photon photoemission. Since the electron wave function in each of these electronic states has a different average distance from the crystal plane, the measurement allowed the step potential at each distance to be sampled. The energy dispersion of the nϭ1 image-potential state was found to be oriented by the ͑111͒ terrace and the nϭ2 state was oriented by the ͑775͒ surface plane. The band structure of the embedded sp-like surface state (nϭ0) was determined by the projection of the bulk band gap onto