The prediction systems under discussion apply when the following conditions obtain: Predictor data are given on the same scale, criterion scores may be given on different scales, and it is necessary to pool data even though criterion scale differences exist. Such a system may be needed for minority group or graduate student prediction where the group sizes are small. Least squares and Bayes methods are used in a cross-validation study conducted for comparison purposes. Data for the study were taken from the files of the Validity Study Service of the College Board. A very limited amount of data were supplied by a few U.S. graduate schools. The Bayes method was better, but it was found that both methods yield negative regression weights; when the absolute values of the weights were used, the methods were both improved and yielded results which were very similar in terms of evaluative statistics computed in the cross sample.