The hafnium-rich portion of the of the hafnium-nitrogen phase diagram is dominated by a substoichiometric rocksalt HfN1-x, the zeta-Hf4N3-x, the eta-Hf3N2-x, and the elemental Hf phase. The zeta and eta nitride phases have a close packed metal atom stacking sequence but their nitrogen atom ordering has yet to be concretely identified. With respect to the composition of these phases, recent computational studies of their phase stability using density functional theory (DFT) are not in agreement with reported experimental observations. In this work, we re-examine the phase stability of the zeta and eta phases using DFT combined with enumerated searches using the known metal atom stacking sequences of these phases but with variable carbon concentration and ordering. We have found new structures for the zeta and eta phases that are now in better agreement with experimental findings. Furthermore, we report a new eta phase,eta-Hf12N7, which lies on the convex hull and has a nitrogen atom ordering that is substantially different from the zeta phase. This work also demonstrates the importance of configurational entropy in dictating the finite temperature phase diagrams in this system.