To obtain a representative set of flow rates for a stream, it is often desirable to fill in missing data or extend measurements to a longer time period by correlation to a nearby gage with a longer record. Linear least squares regression of the logarithms of the flows is a traditional and still common technique. However, its purpose is to generate optimal estimates of each day's discharge, rather than the population of discharges, for which it tends to underestimate variance. Maintenance-of-variance-extension (MOVE) equations [Hirsch, 1982] were developed to correct this bias. This study replaces the logarithmic transformation by the more general Box-Cox scaled power transformation, generating a more linear, constant-variance relationship for the MOVE extension. Combining the Box-Cox transformation with the MOVE extension is shown to improve accuracy in estimating order statistics of flow rate, particularly for the nonextreme discharges which generally govern cumulative transport over time. This advantage is illustrated by prediction of cumulative fractions of total bed load transport.