This paper is devoted to a morphodynamic model of incision into a reservoir deposit driven by partial or total removal of the associated dam. The model considers the erosional processes upstream of the position of the former dam, rather then the deposition that occurs downstream. A theory is developed to predict the evolution of both the width and depth of the incisional channel that develops as erosion progresses. The theory is implemented in a numerical model, which is tested against and verified with flume experiments on sudden, complete removal of a dam. In these experiments a channel of a given initial width is allowed to freely incise into a noncohesive reservoir deposit after sudden dam removal. These experiments show a phenomenon that we refer to as "erosional narrowing." That is, as a channel of a given initial width rapidly incises into the deposit, it can become narrower. As the rate of incision slows, this short period of rapid narrowing is followed by a longer period of widening. In the model the incisional channel is abstracted to a trapezoidal channel with well-defined bed and bank regions, both of which are allowed to erode. Balance between bed and bank erosion plays a key role in the morphodynamics of the channel. More specifically, rapid erosion of the bed can cause the channel to narrow even as bank erosion progresses. As the rate of bed erosion slows, bank erosion causes channel widening. This observed pattern is explained in the context of a theoretical model tested against the experiments.