Low-energy electron-diffraction fine-structure data can often have relatively large inconsistencies associated with the electron-beam incidence conditions. This is in part due to the difficulties associated with working with electrons in the range 40 eV and in part due to the crystal being oriented azimuthally before being put in the vacuum system. The angle of incidence is often measured optically, but the optical and electron paths need not coincide if residual magnetic fields are present. We describe a technique for determining the angles of incidence and azimuth from the data themselves. This relies upon two factors: the ability to vary the azimuth angle continuously and the ability to see two sets of fine-structure features on one I-V scan. This technique is applied to fine-structure data obtained from clean Cu(001) and O/Cu(001) surfaces. We hope that the technique described will help give confidence to those collecting such data that these angles can be uniquely determined and that the data can be usefully analyzed. The uncertainty of not having a technique for this purpose has prevented groups from publishing such data in the past.