These objectives were addressed with field and numerical data derived from a one-dimensional hydraulic model for bankfull and 100-year return interval flood events, supported by closely spaced cross sections for the lower 38-km canyon reach of the Deadwood River (Idaho). Under bankfull conditions, critical energy thresholds for equilibrium floodplain persistence at this study site present the upper limits of: slope = 0.018, shear stress = 175 N/m2, and specific stream power = 400 W/m2. Channel and floodplains near equilibrium, quantified with a near-zero sediment transport divergence (Exner equation), were successfully identified by the minimum unit stream power extremal hypothesis and to a lesser degree by the other extremal hypotheses that minimize energy expenditure (minimum specific stream power, minimum total stream power, and minimum Froude number), provided backwater environments and major tributaries could be identified. Extremal results were compared to hydraulic geometry relations to evaluate how closely equilibrium floodplains approached values for unconfined alluvial river systems.