Multiplicative Kohn-Sham potentials are determined from theoretical electron densities. and the associated orbitals and eigenvalues are used to calculate NMR shielding constants. The shieldings improve as the density varies from Hartree-Fock to MP2 to Brueckner Doubles (BD). Mean absolute errors for isotropic and anisotropic shieldings from ED densities are 16.7 and 8.8 ppm, respectively, compared to correlated ab initio errors of 11.2 and 14.4 ppm. The wavefunction densities are then replaced by Kohn-Sham densities, determined from a hybrid functional. The shieldings are very close to those determined from ED densities and are a significant improvement over conventional hybrid results.