Averages of measurements made in three rivers characterized by a high availability of sediment in relation to runoff, and comparable data that represent the high end of the range of transport rates observed during three sets of laboratory experiments, confirm there is an upper, particle-size-dependent limit to bed-load transport efficiency. Incorporating the regression relation derived from these six diverse and unrelated data sets into R. A. Bagnold's classic formulation yields i(b) = omega [0.0115.D(50)(-0.51)]/0.63. This straightforward scale correlation can be used to estimate the potential rate of bed-load transport (for average conditions) in gravel-bed rivers when sediment transport is constrained neither by the supply of sediment to nor by the amount of sediment available in the channel. The independent application of this empirical limit formula to two rivers with applicable bed-load transport regimes reveals a good (+/-10%) correspondence between average observed and predicted transport rates.