NMR methodology for the measurements of alpha-carbon R-1 and R-1 rho spin relaxation rates in C-13(alpha)-H-alpha and C-13(alpha)-D-alpha spin pairs of U-[C-13; N-15] partially deuterated proteins is developed. The intra-HN[CA] NMR experiment isolates carbon nuclei belonging to either C-13(alpha)-H-alpha or C-13(alpha)-D-alpha spin systems in the same protein sample prior to the measurement of C-13(alpha) relaxation rates. The differences between R-1 and R-2 rates in the two spin pairs (Delta R-1, Delta R-2) eliminate all contributions to C-13(alpha) decay rates not associated with direct C-13(alpha)-H-1(alpha)(D-alpha) dipolar interactions including chemical exchange and serve as robust measures of C-alpha-H-alpha(D-alpha) bond vector motions in proteins. The methodology is applied to the relaxation study of alpha-carbon sites in the protein ubiquitin at two temperatures. The measures of order of individual C-alpha-H-alpha(D-alpha) bond vectors (S-2) in ubiquitin derived from the fitting of differential rates (Delta R-1, Delta R-2) unambiguously report on protein dynamics, thereby eliminating potential contributions from modulations of C-alpha-H-alpha(D-alpha) bond lengths by their environment. They are comparable to the ones obtained from a molecular dynamics simulation at 27 degrees C.