An NMR investigation of proteins with known X-ray structures is of interest in a number of endeavors. Performing these studies through nuclear magnetic resonance (NMR) requires the costly step of resonance assignment. The prevalent assignment strategy does not make use of existing structural information and requires uniform isotope labeling. Here we present a rapid and cost-effective method of assigning NMR data to an existing structure-either an X-ray or computationally modeled structure. The presented method, Exhaustively Permuted Assignment of RDCs (EPAR), utilizes unassigned residual dipolar coupling (RDC) data that can easily be obtained by NMR spectroscopy. The algorithm uses only the backbone N-H RDCs from multiple alignment media along with the amino acid type of the RDCs. It is inspired by previous work from Zweckstetter and provides several extensions. We present results on 13 synthetic and experimental datasets from 8 different structures, including two homodimers. Using just two alignment media, EPAR achieves an average assignment accuracy greater than 80%. With three media, the average accuracy is higher than 94%. The algorithm also outputs a prediction of the assignment accuracy, which has a correlation of 0.77 to the true accuracy. This prediction score can be used to establish the needed confidence in assignment accuracy.