Current methods of determining the rotational diffusion tensors of proteins in solution by NMR spectroscopy exclusively utilize relaxation rate constants for backbone amide 15N spins. However, the distributions of orientations of N-H bond vectors are not isotropic in many proteins, and correlations between bond vector orientations reduce the accuracy and precision of rotational diffusion tensors extracted from 15N spin relaxation data. The inclusion of both 13C alpha and 15N spin relaxation rate constants increases the robustness of the diffusion tensor analysis because the orientations of the C alpha-H alpha bond vectors differ from the orientations of the N-H bond vectors. Theoretical and experimental results for calbindin D9k, granulocyte colony stimulating factor, and ubiquitin, three proteins with different distributions of N-H and C alpha-H alpha bond vectors, are used to illustrate the advantages of the simultaneous utilization of 13C alpha and 15N relaxation data.