  We propose a new generalised Kohn-Sham or constrained hybrid method, where
the exchange potential is the (equally weighted) average of the nonlocal Fock
exchange term and the self-interaction-corrected exchange potential, as
obtained from our constrained minimisation method of semi-local approximations.
The new method gives an accurate single-particle eigenvalue spectrum with an
average deviation between (the negative of) the valence orbital eigenvalues and
the experimental ionisation potentials of about 0.5eV, while the deviation of
core orbitals is within 2eV. The improvement in the eigenvalue spectrum is
achieved with a minimal increase in the total energy.
