NMR spin relaxation of (2)H nuclei in (13)CH(2)D groups is a powerful method for studying side-chain motion in proteins. The analysis is typically carried out with the original model-free (MF) approach adapted to methyl dynamics. The latter is described in terms of axial local motions around, and of, the methyl averaging axis, mutually decoupled and independent of the global motion of the protein. Methyl motion is characterized primarily by the axial squared order parameter, S(axis)2, associated with fluctuations of the methyl averaging axis. This view is shown to be oversimplified by applying to typical experimental data the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Adv. Chem. Phys. 1993, 83, 89) which can be considered the generalization of the MF approach. Neglecting mode coupling and the asymmetry of the local ordering and treating approximately features of local geometry imply inaccurate values of S(axis)2, hence of the residual configurational entropy derived from it. S(axis)2, interpreted as amplitude of motion, was found to range from near disorder to almost complete order. Contrary to this picture, we find with the SRLS approach a moderate distribution in the magnitude of asymmetric local ordering and significant variation in its symmetry. The latter important property can be associated implicitly with the contribution of side-chain rotamer jumps. This is consistent with experimental residual dipolar coupling studies and theoretical work based on molecular dynamics simulations and molecular mechanics considerations. Configurational entropy is obtained in the SRLS approach directly from experimentally determined asymmetric potentials. Inconsistency between order parameters from 2H relaxation and from eta(HC-HH) cross-correlation and increase in order parameters with increasing temperature were observed with the MF approach. These discrepancies are reconciled, and physically tenable temperature dependence is obtained with the SRLS approach.