Vertical ionization energies of C-60 and C-70 fullerenes are calculated with semidirect implementations of electron propagator methods and a triple-zeta plus polarization basis set. These predictions are in close agreement with photoelectron spectra for final states in which the Koopmans description is qualitatively valid. Many correlation states, where the latter description fails, are predicted by methods with nondiagonal self-energies. (c) 2008 American Institute of Physics.