In order to obtain chemical insight from shifts in core-ionization energies, DI, it is often desirable to separate the initial-state contribution, DV, from that caused by relaxation in the final state, DR. These quantities are related through DI 5 DV 2 DR. Whereas the chemical shift itself, DI, may be measured very accurately, the scope of the present contribution is to provide a tool for accurate quantification of the initial-state contribution DV to the measured shift. Common procedures of estimating DV either from Hartree-Fock orbital energies or from electrostatic potentials at nuclear positions are examined. Whereas orbital energies suffer from the neglect of valence-electron correlation, the use of electrostatic potentials does not take proper account of the finite extension of core orbitals. In order to circumvent both of these problems, a reformulation valid for any valence-correlated wave function is presented for V, the energy needed to remove a core electron without relaxation of spectator electrons. The resulting expression may be seen as an extension of Koopmans' theorem, and reduces to the former in the case of a Hartree-Fock wave function. This extended Koopmans' theorem is used to compare initial-state effects in X-ray photoelectron spectra for a set of simple hydrocarbons.