During bed-load transport by overland flow, momentum is transferred from the flow to the bed via grain collisions, resulting in a decrease in flow velocity and an increase in flow resistance, herein termed bed-load transport resistance. In overland flow on mobile plane beds, total flow restistance f consists of grain resistance f_g and bed-load transport resistance f_bt. In order to identify and evaluate the relative importance of the factors controlling f_bt, 38 flume experiments were performed on slopes of 2.7 and 5.5º using sediment with median diameters of 0.74 and 1.16 mm. All flows were supercritical and turbulent. This study is an extension of a recent study by Gao and Abrahams (Earth Surface Processes and Landforms 2004, vol. 29, pp. 423-435). These authors found that f_bt is controlled by three factors: sediment concentration C, dimensionless sediment diameter D_*, and relative submergence h/D, where h is flow depth, D is median sediment diameter. However, a new dimensional analysis identifies two additional factors: Froude number F and slope S. Multiple regression analyses reveal (1) that these five factors together explain 97 per cent of the variance of f_bt, and (2) that S control f_bt entirely through C. The variable C is therefore redundant, and a new functional equation relating f_btto D_*, h/D, S and F is developed. This equation may be used to predict f_bt. An advantage of this equation is that it may be used to predict f_bt without measuring bed-load transport rate. Copyright © 2004 John Wiley & Sons, Ltd.