Ab initio one-, two-, and three-bond C-C, C-N, and N-N spin-spin coupling constants, and one-bond C-H and N-H coupling constants have been computed using two different theoretical methods, SOPPA/ (qzp,qz2p) and EOM-CCSD/(qzp,qz2p). Both EOM-CCSD (equation-of-motion coupled cluster singles and doubles) and SOPPA (second-order polarization propagator approximation) coupling constants correlate linearly with experimental data. In the great majority of cases, the computed EOM-CCSD C-C, C-N, N-N, and N-H coupling constants are in better agreement with experimental data than SOPPA values, although both levels of theory provide reasonable estimates of these couplings. EOM-CCSD consistently underestimates one-bond C-H coupling constants by about 10 Hz, and SOPPA values of 1 J(C-H) are in better agreement with experimental data. The performance of SOPPA supports its use in future studies of coupling constants involving C, N, and H in larger chemical and biological systems. † Part of the "Rusell M. Pitzer Festschrift".