The indirect nuclear spin-spin coupling constants of C2H4, CH2NH, CH2O, and CH2S were investigated by means of correlated ab initio calculations 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) using large basis sets, which are optimized for the calculation of coupling constants. It is found that at the self-consistent-field (SCF) level CH2NH and CH2S exhibit triplet instabilities whereas CH2CH2 and CH2O show triplet quasi-instabilities, which renders the SCF results meaningless. Our best results deviate between 0.3 and 2.7 Hz from the experimental values. We find that although the one-bond C-H and Y-H couplings as well as the two-and three-bond H-H couplings are dominated by the Fermi contact term, significant contributions of the orbital paramagnetic and sometimes even spin-dipolar terms are observed for the one-bond C-Y and two-bond C-H and Y-H coupling constants. Similarly the changes in the couplings caused by the electronegativity and the lone-pair of Y are mostly due to changes in the Fermi contact (all couplings) and the orbital paramagnetic contribution (C-Y and two-bond Y-H couplings). However, the trend in the changes are neither the same for both terms not for all couplings. In particular, the position of CH2S in the series varies indicating that either the electronegativity or the lone pairs are the dominating perturbation. Furthermore, small but optimized Gaussian basis sets for the calculation of indirect nuclear spin-spin coupling constants are presented. They were obtained by contraction of the s- and p-type basis functions for C, N, O, and S and of the s-type basis functions for H of the large uncontracted basis sets. Molecular orbital coefficients of self-consistent-field calculations on CH4, NH3, H2O, H2S, and H-2 with the uncontracted basis sets were used as contraction coefficients. Applied in the calculation of all coupling constants in C2H4, CH2NH, CH2O, and CH2S the contraction leads to a maximum basis set error of similar to0.5 Hz.