The river step is an important driver for geomorphic evolution in bedrock rivers, but the effect that variations in channel geometry upstream and downstream of a river step have on hydraulic jump regime and energy dissipation has not previously been investigated. The associated hydraulic jump is inherent to a river step and its regime is a primary control on step morphodynamics. In turn, the hydraulic jump regime is controlled by several variables as detailed in a new conceptual framework herein. Also in this study, a parsimonious semianalytical numerical model of step hydraulics is developed to quantify energy dissipation and delineate hydraulic jump regimes, accounting for discharge, jump submergence, and nonuniform channel geometry through a step. Despite remaining limitations in step theory, the model simulates how natural steps respond to a wide range of conditions. The model shows that hydraulic jump regime and energy dissipation exhibit greater sensitivity to channel nonuniformity as discharge increases and/or step height decreases. Also, channel conditions that create greater jump submergence lead to decreased energy dissipation, regardless of the discharge regime. The model also reinforces the common observation about gully erosion that downstream channel widening enhances upstream knickpoint migration. The new algorithm may be used to aid river engineering involving steps and could be useful for landscape evolution modeling.