The abandonment of terraces in incising alluvial rivers can be used to infer tectonic and climatic histories. A river incising into alluvium erodes both vertically and laterally as it abandons fill-cut terraces. We argue that the input of sediment from the valley walls during entrenchment can alter the incision dynamics of a stream by promoting vertical incision over lateral erosion. Using a numerical model, we investigate how valley wall feedbacks may affect incision rates and terrace abandonment as the channel becomes progressively more entrenched in its valley. We postulate that erosion of taller valley walls delivers large pulses of sediment to the incising channel, potentially overwhelming the local sediment transport capacity. Based on field observations, we propose that these pulses of sediment can form talus piles that shield the valley wall from subsequent erosion and potentially force progressive channel narrowing. Our model shows that this positive feedback mechanism can enhance vertical incision relative to 1-D predictions that ignore lateral erosion. We find that incision is most significantly enhanced when sediment transport rates are low relative to the typical volume of material collapsed from the valley walls. The model also shows a systematic erosion of the youngest terraces when river incision slows down. The autogenic entrenchment due to lateral feedbacks with valley walls should be taken into account in the interpretation of complex-response terraces.