Anabranching rivers have been identified globally, but a widely accepted and convincing theoretical explanation for their occurrence has remained elusive. Using basic flow and sediment transport relations, this study analyzes the mechanisms whereby self-adjusting alluvial channels can anabranch to alter their flow efficiency (sediment transport capacity per unit of stream power). It shows that without adjusting channel slope, an increase in the number of channels can produce a proportional decrease in flow efficiency, a finding particularly relevant to understanding energy consumption in some braided rivers. However, anabranching efficiency can be significantly increased by a reduction in channel width, as occurs when vegetated alluvial islands or between-channel ridges form. The counteracting effects of width reduction and an increasing number of channels can cause, with no adjustment to slope, an otherwise unstable system (underloaded or overloaded) to achieve stability. As with other river patterns, anabranching can be characterized by stable equilibrium or accreting disequilibrium examples.