The continuous probability distribution (CUPID) method [Dzakula, Z; Westler, W. M.; Edison, A. S.; Markley, J. L. J. Am. Chem. Sec. 1992, 114, 6195] for conformational analysis of molecules from nuclear magnetic resonance (NMR) data has been extended to the determination of molecular conformations of five-membered rings. This approach, which should be particularly useful for studies of molecules containing pyrrolidine or furanose rings, is illustrated by the analysis of NMR data from the literature for small peptides containing L- and B-prolines, hydroxyprolines, and fluoroprolines. The CUPID approach to the analysis of five-membered rings, which takes advantage of linear regression, generally yields better fits to experimental data in a shorter time than the conventional discrete approach, which utilizes nonlinear fitting procedures. The new method proved successful in a few cases in which the conventional approach failed to produce satisfactory analysis of the data. Built-in error-propagation analysis in the CUPID software provides a direct assessment of the reliability of the calculated results.