The distribution of the deviation of calculated from measured nuclear Overhauser effect (NOE) intensities is a priori unknown. The use of a log-normal distribution to describe these deviations permits the direct calculation of a structure from the measured intensities without first converting them into distance bounds. We show that the log-normal distribution is a natural choice for describing errors in NOE data and that it improves the accuracy, precision, and quality of the calculated structures compared to the usual bounds representation.