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Very-low-energy electron diffraction (VLEED) is a direct probe for the unoccupied electronic band structureE(k) corresponding to the upper bands of photoemission (PE). These bands can contain significant non-free-electron and self-energy effects. Use of the experimental VLEED bands in PE and inverse PE allows to determine the valence and conduction bandE(k) absolutely, i.e. with complete and approximation-free control of the 3D wavevector k.