Our recently developed method for the calculation of indirect nuclear spin-spin coupling constants is studied in more detail. For the couplings between nuclei other than N, O, and F (which have lone pairs) the method yields very reliable results. The results for (1)J(SI-H) couplings are presented and their dependence on the basis set quality is analyzed. Also, (2)J(H-H) and (1)J(X-H) couplings (X=C, Si, Ge, Sn) in XH(4) molecules are presented and the relativistic effects on (1)J(X-H) are discussed. The limitations of the method, which is based on density functional theory, are connected with the inability of the present LDA and GGA exchange-correlation functional to describe properly the spin-perturbations (through the Fermi-contact mechanism) on atoms to the right of the periodic table (containing lone pairs). However, the deviations from experiment of the calculated couplings for such nuclei are systematic, at least for one-bond couplings, and therefore these calculated couplings should still be useful for NMR structure determinations.