We present a multilayer model for the interpretation of ARXPS data in which the total atom density of each layer is not constrained. We find that the variable density profiles can be successfully stabilized by the use of Tikhonov-c(2) regularization and a value for the regularization parameter for which the chi(2) statistic for the goodness of fit to the data is equal to the number of independent observations in the data set. (C) 2008 Elsevier B.V. All rights reserved.