We report on an electron-pair emission study from a Cu(111) surface excited by electron impact with different primary electron energies. We identify in the energy spectra, features that can be directly related to the underlying band structure. This, in turn, proves an important assumption in the theoretical description of the pair-emission process, namely that an effective single-particle picture for the electronic structure is an adequate description. With this observation, it is possible to identify the orbital character of the participating valence state. The relative pair-emission intensity from the surface state and 3d states is observed to vary dramatically with the primary energy. We observe particular conditions where the contribution from the Shockley surface state is strong. We propose a simplified model to explain this observation.