AbstractA modification of the PLS1 algorithm is presented. Stepwise optimization over a set of candidate loading weights obtained by taking powers of the y–X correlations and X standard deviations generalizes the classical PLS1 based on y–X covariances and hence adds flexibility to the modelling. When good linear predictions can be obtained, the suggested approach often finds models with fewer and more interpretable components. Good performance is demonstrated when compared with the classical PLS1 on calibration benchmark data sets. An important part of the comparisons is managed by a novel model selection strategy. The selection is based on choosing the simplest model among those with a cross‐validation error smaller than the pre‐specified significance limit of a χ2‐statistic. Copyright © 2005 John Wiley & Sons, Ltd.