It is now generally accepted that deltas that prograde to the shelf edge are able to transport coarse sediment to deep water either with or without sea level changes. However, it is still unclear how feeder rivers behave differently in the shelf-edge delta case to rivers found in a delta that progrades over the shelf. A series of nine shelf-edge delta experiments are presented to investigate the lateral mobility of the feeder channel at the shelf edge and the associated deep water depositional system under a range of sediment supply rates and shelf-front depths. In the experiments, constant sediment supply from an upstream point source under static sea level led the fluviodeltaic system to prograde over the shallow shelf surface and advance beyond the shelf edge into deep water. The feeder river of the fluviodeltaic system became a bypass system once the toe of the delta front reached the shelf edge. After the delta front was perched at the shelf edge, a submarine fan developed in deep water although remaining disconnected from the delta. In this bypass stage, no regional avulsion or lateral migration of the feeder river occurred and all sediment from the upstream source bypassed the river, delta front, and shelf-front slope. The duration of the bypass stage is proportional to shelf-front depth and inversely proportional to sediment discharge. The combined duration of the shelf-transit phase of the fluviodeltaic system and the bypass phase is the characteristic time scale for the continental margin to “anneal” transgression-inducing perturbation due to high-frequency and/or high-amplitude relative sea level rise. The sequential evolution in the experiment compares favorably to the Eocene Sobrarbe Formation, a shelf-edge delta in Spain, although natural variations are noted. This comparison justifies the application of concepts proposed herein to natural systems and provides insight into interpreting processes from ancient shelf-edge delta systems.