Operational procedures for the Graduate Record Examinations Validity Study Service are reviewed, with emphasis on the problem of frequent occurrence of negative coefficients in the fitted within-department regressions obtained by the empirical Bayes method of H. I. Braun and D. Jones (1985). Several alterations of the operational procedures are proposed that would reduce the frequency of negative coefficients, and, if desired, completely eliminate them. It is argued, however, that there are no a priori reasons for assuming that all the coefficients are nonnegative. Reports of the fitted within-department regressions should be based on a single model, that would be found by model exploration. The estimation procedures could be improved by employing more flexible software for modeling between-department variation. Appendixes describe extended shrinkage in the empirical Bayes estimation and give common within-department variance. (Contains 2 tables, 5 figures, and 13 references.) (Author/SLD)