The surface-potential barrier shape for the (001) face of copper was determined by an analysis of low-energy-electron-diffraction fine-structure measurements. The fitting of the fine-structure spectra was performed with a precise knowledge of the incident diffraction conditions of the experimental data (incidence angle, azimuthal angle, and contact-potential difference). This precision is necessary to allow a consistent barrier shape to be determined. For three different angles of incidence, it was found that a good match between theoretical and experimental I-V spectra was obtained when the image plane was located 2.5 a.u. from the topmost layer of atoms.