Contrary to the popular belief that stream power determines whether a river incises through or diverts around an evolving bedrock uplift, we propose that river sediment flux tectonic uplift rate are the most influential variables. We construct a simplified theoretical model of an equilibrium alluvial river system responding to local bedrock uplift by coupling a diffusion model describing the alluvial river with a kinematic wave model describing the incising bedrock river. The initial uplift reduces local river gradient, causing the river to deposit sediment in the accommodation space created upstream. At the same time, the river incises into the uplifting bedrock, starting from a knickpoint at the downstream edge of the uplift. The sediment aggradation must keep pace with the uplift rate until the incision has propagated through to the upstream edge of the bedrock block; otherwise the river will divert to another course. We use geometric arguments to identify sediment flu ∧ uplift rate as the controlling variables of the system.