The general description of simultaneous electron-impact ionization–excitationprocesses is reformulated in terms of an irreducible tensor representation. Using anumerical model, in which the interaction between a ‘fast’ ionizing projectile andthe target is described by first-or second-order plane-wave and distorted-wavemodels, combined with a convergent close-coupling-type description of the initialbound state and the interaction between a ‘slow’ ejected electron andthe residual ion, new benchmark calculations for the (e, e′γ)process have been performed. The predictions are compared with recentexperimental data on ionization–excitation of helium. The similarity to results forexcitation processes and the potential extension of propensity rules is discussed.