Rational regime relationships for the width, depth and slope of a river in equilibrium are developed using the Ackers and White sediment transport formula and the White, Paris and Bettess friction relationships, together with a principle of maximum sediment transporting capacity. This concept of maximising the sediment transporting capacity is shown to be equivalent to minimising the slope of the river. The relationships which are developed show good agreement with other empirically derived regime relationships and data from sand channels. Some comparisons are made with data from gravel rivers and the difficulties in applying regime concepts to these rivers are discussed.