The effect of triple excitations in coupled-cluster calculations of indirect spin-spin coupling constants is investigated in coupled-cluster singles and doubles (CCSD) calculations augmented by a perturbative treatment of triples [CCSD(T)], in calculations based on the CC3 model as well as in coupled-cluster singles, doubles, and triples (CCSDT) calculations. Though triple excitation effects are in most cases not particularly pronounced, it is demonstrated that among the approximate schemes for handling triples only the CC3 model with no orbital relaxation included (unrelaxed CC3) provides an adequate description. The otherwise successful CCSD(T) aproach appears to either significantly overestimate triple excitation effects or to yield corrections with the wrong sign in comparison to CCSDT.