Neutron elastic and inelastic scattering cross sections of elemental iron were measured from 1.5 to 4.0 MeV with incident neutron resolutions of ≲50 keV and at incident neutron energy intervals of ≲50 keV. Cross sections for the excitation of observed levels at 0.853, 1.389, 2.097, 2.579, 2.677, 2.974, and 3.152 MeV are determined. The observed elastic and inelastic scattering angular distributions fluctuate strongly with incident energy. The experimental results are averaged over broad energy intervals and are compared with the predictions of spherical optical statistical and coupled-channel models, including consideration of direct inelastic excitations. The importance of a comprehensive data base in such energy-averaged interpretations and in the evaluation of data for technological use is stressed.