Working equations for a spin-restricted coupled-cluster (SR-CC) ansatz with full inclusion of triple excitations are presented. The equations have been derived using a new formulation of the SR-CC theory that is equivalent to the original one but much easier processed and also provides a new interpretation of the underlying concepts of the SR-CC approach. Test calculations with a preliminary SR-CC singles, doubles, triples (SR-CCSDT) implementation indicate that spin-restriction has a rather small effect on the computed energies and that the effects are-as expected-less pronounced than in the case of the CC singles, doubles approximation. The corresponding partially spin-adapted scheme turns out less accurate and is shown in CCSDT calculations to be incorrect in the untruncated limit.