Experiments carried out in a flume at St. Anthony Falls Laboratory, University of Minnesota have shown an interesting phenomenon that we refer to as "erosional narrowing". This occurs immediately after the sudden removal of a dam that is filled with sediment. A channel incises into the deposit after failure of the leading front of the sediment deposit. In the early stages of incision this channel may become significantly narrower as it undergoes degradation. Both incision and narrowing propagate upstream on a relatively short time. In the long term however, the depositional contribution from the side slopes eventually balances and then surpasses erosional narrowing, so the channel widens toward some new equilibrium state with a lower streamwise slope. This picture is at variance with the general belief that the incisional channel widens from the very beginning. A simplified 1-D model of the phenomenon is developed and implemented numerically; in it the time evolution of channel width depends on the streamwise gradient of sediment transport and fluvial erosion of the channel banks (sidewalls).