Abstract The general tendency for sediment supply to deep water to be relatively high during eustatic fall and lowstand, and relatively low during rise and highstand, is recognized in the sequence-stratigraphy literature. Much less is known about the cumulative effect of repeated eustatic cycles on net deep-water sediment delivery. Here we investigate the net effect of offshore sediment delivery during a complete eustatic cycle, which we term sediment pumping , and the possibility of cumulative sediment pumping if repeated eustatic cycles increase the net delivery of sediment to deep water averaged over several cycles. We measure sediment pumping in terms of net offshore delivery after one or more complete eustatic and associated cycles relative to delivery in the absence of cycles. Combining data from a quasi-2D laboratory experiment and a 2D geometric model, we find that net sediment pumping over isolated and superimposed base-level cycles of variable period varies from somewhat negative to strongly positive, depending on (1) time period of imposed base-level cycle, (2) sense of rotation of the spatial subsidence pattern, and (3) the phase of sediment supply relative to eustatic variation. A relatively short-period base-level cycle (i.e., period less than the basin equilibrium time) increases net pumping (relative to the constant base-level reference case) whereas a relatively longperiod cycle yields no or even negative net pumping. Short-period base-level cycles superimposed on a long-period cycle produce a strong net offshore sediment pumping. Other factors being equal, base-level cycles with basin subsidence cause substantially greater net pumping in backtilted basins than in foretilted ones. When sediment supply varies over a base-level cycle, pumping is maximized when the sediment-supply maximum occurs during eustatic falling stage or lowstand. External Controls on Deep-Water Depositional Systems SEPM Special Publication No. 92 (CD version), Copyright © 2009 SEPM (Society for Sedimentary Geology), ISBN 978-1-56576-200-8, p. 41–56.