The morphology of bedrock river channels is controlled by climatic and tectonic conditions and substrate properties. Knowledge of tectonic controls remains scarce. This is partly due to slow tectonic rates and long response times of natural channels and partly due to the difficulty in isolating and constraining tectonic forcing conditions in the field. To study the effect of tectonic forcing on channel geometry, we have developed a numerical model of the cross-sectional evolution of a detachment-limited channel. Its predictions are matched by an analytical model based on the assumption of the minimization of potential energy expenditure. Using these models, we illustrate how local tectonics can alter the observed width-discharge scaling and discuss published field data in light of our findings. Except for one case, the models fail to correctly describe field observations of well-constrained cases. This implies that the shear stress/stream-power family of models is too simple to describe the behavior of natural channels. Additional complexities such as sediment effects and discharge variability exert a strong control on channel morphology and need to be taken into account in the modeling of channel dynamics and steady state.