A new approach to rotational-echo double-resonance (REDOR) data analysis, analogous to Boltzmann maximum entropy statistics, is reported. This Boltzmann statistics REDOR (BS-REDOR) approach is useful for reconstructing an unbiased internuclear distance distribution for multiple internuclear distances from experimentally limited REDOR data sets on isolated spin pairs. The analysis is characterized by exploring reconstructions on model data and applied to both [1-C-13,N-15]-glycine and a long intramolecular distance in A beta (16-22) peptide nanotubes. The approach also provides insight into the minimal number of REDOR data points required to allow faithful determination of dipolar couplings in systems with multiple internuclear distances.