Most importantly, we find that an empirically-shifted version of the conventional STM reduces the aforementioned errors below 0.2 eV for a variety of functionals. The value of this shift depends on the atomic number, consistent with theoretical considerations. Importantly, this approach requires only two SCF calculations: a conventional one for the ground state of the neutral molecule, following by a single, edge-specific fractional-electron calculation for the core-ionized state. This is a cost comparable to that of ∆SCF and affords accuracy that is competitive with the best variants of GW , all of which are considerably more expensive. Tests for a variety of main-group compounds suggest that this shifted-STM approach affords accurate chemical shifts as well.