AbstractIn many applications it is expected from theory that a signal should be non‐negative and unimodal, that is, show only one peak. If the data are noisy, standard smoothing algorithms will not always give the desired result: peaks may be rounded and negative lobes may occur in the tails. Positive unimodal fits can be obtained by modeling the logarithm of a curve and combining a standard roughness penalty with a specialized asymmetric penalty. The theoretical basis and implementation in Matlab are presented, as well as performance on real and simulated data. Copyright © 2006 John Wiley & Sons, Ltd.