Spectroscopic constants have been determined for 13 first row diatomic hydrides using coupled cluster theory with explicit inclusion of (iterative) triple excitations (CCSDT). Comparison of the predicted dissociation energies, bond lengths, harmonic frequencies, and anharmonicities was made with experiment and other high-level theoretical treatments. These include complete active space configuration interaction wave functions, coupled cluster theory with perturbative triples [CCSD(T)], and new benchmark full configuration interaction calculations. Excellent overall agreement with experiment was found, even without correcting for small changes due to core/valence and relativistic effects. The intrinsic CCSDT error with respect to experiment for each molecule and property was estimated by extrapolating to the complete basis set limit. Among the various properties examined in this study, no significant differences were found between CCSD(T) and CCSDT. In light of the substantial increase in computational cost associated with the latter method, there appears to be little justification for selecting it over CCSD(T) in studies of first row hydrides. Preliminary results for first row diatomics, e.g., N-2, suggest that the impact of CCSDT will increase with the number of electrons. (C) 2000 American Institute of Physics. [S0021-9606(00)31513-6].