Recombinant HIV-1 protease was obtained from bacteria grown on a 98% D2O medium containing 3-C-13 pyruvic acid as the sole source of C-13 and H-1, The purified protein is highly deuterated at non-methyl carbons, but contains significant populations of (CHD2)-C-13 and (CH2D)-C-13 methyl isotopomers. This pattern of isotope labeling permitted measurements of H-1 and C-13 relaxation rates of (CHD2)-C-13 isotopomers and H-2 (D) relaxation rates of (CH2D)-C-13 isotopomers using a single sample. The order parameters S-axis(2), which characterize the motions of the methyl rotation axes, were derived from model-free analyses of R-1 and R-2 data sets measured for C-13 and H-2 spins. Our primary goal was to compare the S-axis(2) values derived from the two independent types of data sets to test our understanding of the relaxation mechanisms involved. However, S-axis(2) values derived from the analyses depend strongly on the geometry of the methyl group, the sizes of the quadrupolar and dipolar couplings, and the effects of bond vibrations and librations on these couplings. Therefore uncertainties in these basic physical parameters complicate comparison of the order parameters. This problem was circumvented by using an experimental relationship, between the methyl quadrupolar, C-13-C-13 and C-13-H-1 dipolar couplings, derived from independent measurements of residual static couplings of weakly aligned proteins by Ottiger and Bar (J. Am. Chem. Soc. 1999, 121, 4690-4695) and Mittermaier and Kay (J. Am. Chem. Sec. 1999, 121, 10608-10613). This approach placed a tight experimental restraint on the values of the H-2 quadrupolar and C-13-H-1 dipolar interactions and greatly facilitated the accurate comparison of the relative values of the order parameters. When applied to our data this approach yielded satisfactory agreement between the S-axis(2) values derived from the C-13 and H-2 data sets.