Abstract. We present correlated calculations of the indirect nuclear spin-spin coupling constants of HD, HF, H2O, CH4, C2H2, BH, AlH, CO and N2 at the level of the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes SOPPA(CCSD). Attention is given to the effect of the so-called W4 term, which has not been included in previous SOPPA spin-spin coupling constant studies of these molecules. Large sets of Gaussian basis functions, optimized for the calculation of indirect nuclear spin-spin coupling constants, were used instead of the in general rather small basis sets used in previous studies. We find that for nearly all couplings the SOPPA(CCSD) method performs better than SOPPA.