The Saupe matrix describing protein alignment in a liquid-crystalline medium contains five independent elements, enabling the generation of up to five linearly independent alignment conditions. Measurement of internuclear residual dipolar couplings by NMR spectroscopy under these conditions, orthogonal in five-dimensional alignment space, provides access to the amplitude, asymmetry, and direction of motions of the internuclear vector. It is demonstrated for the small protein domain GB3 (56 residues) that suitably orthogonal alignment conditions can be generated in a single liquid-crystalline medium of Pf1 phage, by generating a series of conservative mutants that have negligible impact on the time-averaged backbone structure of the domain. Mutations involve changes in the charge of several solvent-exposed side chains, as well as extension of the protein by either an N- or C-terminal Histag peptide, commonly used for protein purification.