The two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for NMR relaxation in proteins is extended to derive conformational entropy, S. This version of SRLS is applied to deuterium relaxation from the C-CDH2 bonds of free and peptide-bound PLC(gamma)1C SH2. Local C-CDH2 motion is described by a correlation time for local diffusion, tau(2), and a Maier-Saupe potential, u. On average, tau(2), which largely fulfills tau(2) << tau(1)(tau(1) - correlation time for global tumbling), is 270 +/- 41 ps and u is 2 +/- 0.1 kBT. The PLC(gamma)1C SH2 data were analyzed previously with the model-free (MF) method. SRLS is a generalization of MF, assumed so far to yield the latter for tau(2) << tau(1) and simple local geometry. Despite these conditions being fulfilled, we find here that r2 and u differ substantially from their MF counterparts. This is shown to stem from MF (a) disregarding mode-coupling of the first type (see below) and (b) parametrizing the methyl-moiety-related spectral density function (SDF). Our main interest lies in Delta S, the conformational entropy difference between the peptide-bound and free PLC(gamma)1C SH2 forms. We find that Delta S is rendered inaccurate in MF because factors a and b above impair the accuracy of Sa, the parameter on which the calculation of Delta S is based. Conformational entropy was obtained previously using various simple system-specific models. SRLS is unique in obtaining this important thermodynamic quantity based on a general physically well-defined local potential. It is also unique in its ability to extract the information inherent in H-2 relaxation parameters from methyl moieties in protein with accuracy commensurate with data sensitivity.