The relation between equilibrium stream channel morphology and three independent governing variables, discharge, sediment supply, and valley slope, is investigated using a stream table. The experiments are based on a generic physical model of a laterally active gravel bed stream and directed by a recently published rational regime model. While a variety of channel adjustments are possible, the primary adjustment observed was in the channel slope. Other adjustments, such as surface armor composition and cross-sectional shape, were minor in comparison. The equilibrium slope is well predicted by a linear function of sediment concentration which is bounded by two thresholds: one associated with the minimum stream power necessary to deform the bed and the other associated with the maximum sediment feed that can be transported by the available flow. The results suggest that the system tends to move toward the minimum slope capable of transporting the sediment supply, in the process increasing the flow resistance for the system. Whether or not a minimum slope or a maximum system-scale flow resistance is reached cannot be determined given the available data, but there appears to be a unique slope (or, at least, a limited range of slopes) for which a stable alluvial channel morphology can be established for a given sediment concentration. The implications of this behavior are evaluated for the theoretical basis of the extremal hypothesis used to close the formulation of a rational regime model.