Calculations of 11 diatomic dissociation energies with coupled cluster theory through iterative triple excitations highlight both the strength and limitations of this method. By combining very large basis sets (through septuple zeta in some cases) and complete basis set extrapolations with corrections for core/valence correlation, scalar relativistic and atomic/molecular spin-orbit effects, it was possible to achieve excellent agreement with experiment in most cases. However, for C-2 and CN the extent of the multiconfigurational nature of the molecules caused problems for the single configuration-based couple cluster methods. In the worse case, the inclusion of iterative triples resulted in a change with respect to the perturbative triples result which was of the opposite sign to the full configuration interaction change. This work emphasizes the difficulties in achieving uniform chemical accuracy even for ground state, first and second row diatomics.