We combine a perturbational calculation, using spin-orbit pseudopotentials, of the spin-orbit effect on nuclear shieldings with scalar relativistic effects taken into account self-consistently using quasirelativistic pseudopotentials. The shieldings are calculated for light nuclei in systems containing heavy atoms, for which matching spin-orbit and quasirelativistic pseudopotentials are used. The second-order spin-orbit contribution arising from the magnetic field dependence of the one-electron spin-orbit Hamiltonian is-also included. The method is implemented within the framework of density-functional theory and is capable of treating large molecular systems economically. Calculations are presented for the HX and CH3X (X = F, Cl, Br, I) molecules, third-row transition metal carbonyls, and a series of methyl mercury compounds.