Laboratory experiments lead to a way of modifying two existing transport rate formulae so that transport rates and size distributions of transported material can be predicted knowing the hydraulic conditions and the bed-material grain size distribution. The Ackers and White and the Paintal transport formulae are modified accordingly and used successfully on laboratory data. Difficulties in defining bed-material distributions and the possibility of overpassing in sand/gravel systems are reflected in the results obtained using data from four rivers.