Multiphoton photemission, scanning tunneling spectroscopy, and first-principles electronic structure calculations have been applied to determine the dispersion of the occupied and unoccupied Shockley surface state of Cu(111). The dispersion deviates significantly from the paradigmatic parabolic behavior of quasi-free electrons with increasing energy above the Fermi level. Based on our calculations, we ascribe this deviation to the shift of the spectral weight of the surface state into the bulk, and of bulk states toward the surface, which leads to an enhanced hybridization between the states with increasing energy.