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Photoelectron spectroscopy, especially at pulsed sources, is ultimately limited by the Coulomb interaction in the electron cloud, changing energy and angular distribution of the photoelectrons. A detailed understanding of this phenomenon is crucial for future pump–probe photoemission studies at (x-ray) free electron lasers and high-harmonic photon sources. Measurements have been performed for Ir (111) at hν= 1000 eV with photon flux densities between∼ 10 2 and 10 4 photons per pulse and μm 2 (beamline P04/PETRA III, DESY Hamburg), revealing space-charge induced energy shifts of up to 10 eV. In order to correct the essential part of the energy shift and restore the electron distributions close to the Fermi energy, we developed a semi-analytical theory for the space-charge effect in cathode-lens instruments (momentum microscopes, photoemission electron microscopes). The theory predicts a Lorentzian …