Abstract Climate and tectonics determine the amount of discharge and sediment delivery to rivers. They also affect the temporary storage of sediment, because gradients of valley floors are adjusted to the amount of bedload and the amount of discharge, and thus control the delivery of sediment to the coast. Can the history of sediment accumulation on the coastal plain and shelf help to reconstruct the history of discharge and sediment flux that produced it? Results from both field studies and model studies seem ambiguous and contradictory in that convincing evidence is presented against as well as in favor of distinct, correlatable, climate-induced signals in the stratigraphy at river mouths. We have studied the effects of pulses of discharge and sediment influx on the gradient of the river-valley system on different time scales by analogue modeling experiments. Discharge and sediment load were increased and decreased independently, and the impact of these changes on the valley gradient and on the sediment flux at the valley mouth were measured. Changes in discharge as well as sediment flux into the system cause predictable increases and decreases in the gradient of the valley floor. However, fundamental differences between the response of the sediment flux at the river mouth to changes in discharge and to changes in sediment flux, and differences between the history of total mass accumulation in response to changes in discharge and sediment flux, emerge. The first fundamental difference between the response to change of discharge and the response to change of sediment input is the total sediment budget at the valley outlet. The second fundamental difference is that the gradient of the valley floor is positively correlated with sediment influx, and negatively with discharge. Hence, by establishing the history of total sediment flux at the valley outlet in combination with a reconstruction of gradients in the river valley (e.g., through reconstruction of terraces) constraints can be put on discharge and sediment flux through time. The third difference is that the response to changes of discharge is very rapid, whereas the response to changes of sediment flux is much slower. Combined with the difference in impact on sediment flux at the valley outlet of the river system, this causes the high-resolution stratigraphy in the delta-shelf realm to be controlled by high-frequency (climate) changes in discharge and the low-resolution stratigraphy by low- frequency (tectonic) changes in sediment flux.