A new approach to the quantitative experimental analysis of conformational distributions in partially ordered biopolymers is described and used to determine the fractional contents of alpha-helical, 3(10)-helical, and random coil components in the conformational distributions of a 17-residue helix-forming peptide [Marqusee, S.; Baldwin, R. L. Proc. Natl. Acad. Sci., U.S.A. 1987, 84, 8898-8902]. The approach is based on solid-state NMR measurements that probe phi and psi dihedral angles at specific isotopically labeled sites, in particular two-dimensional magic-angle spinning NMR exchange spectra, carried out on glass-forming frozen solutions in glycerol/water. The data analysis employs a combination of constrained molecular dynamics simulations, to generate model dihedral angle distributions, and Bayesian statistics, to permit a quantitative determination of the relative probabilities of the possible fractional contents of alpha-helical, 3(10)-helical, and random coil components. The peptide is found to be highly alpha-helical in pure glycerol/water at low temperatures. Addition of urea has the primary effect of converting alpha-helical conformations to 3(10)-helical conformations, rather than to random coil conformations. These results provide experimental evidence for the role of 3(10)-helices as thermodynamic intermediates in the folding and unfolding of alpha-helical segments in peptides and proteins.