The geologic record from high-latitude continental margins shows that soft-bedded ice streams are capable of eroding, transporting, and depositing large volumes of sediment. Interpretation of these records relies on correct understanding of how sediments were transferred. We use a three-dimensional numerical ice-flow model, with physically based processes taking place in a Coulomb-plastic basal till layer, to test a new hypothesis related to sedimentary processes occurring beneath ice streams. Based on recent observations of a 15-m-thick debris-bearing basal ice layer (Bit) in Kamb Ice Stream, Antarctica, we propose that sediment entrainment by freeze-on, followed by englacial transport, and eventually meltout, represent efficient mechanisms whereby ice streams erode their bed and redistribute sediments. Our experimental setup produces results where ice stream flow is characterized by oscillations between fast and stagnant modes of flow. We show that there is a strong coupling between the amplitude of the ice stream oscillations and the amount of sediment eroded and transferred out of the modeled system due exclusively to the formation and advection of a BIL. We also show that increased incorporation of water from a basal water system amplifies the oscillations and thus the growth of the BIL. The patterns of ice stream flow, and associated sediment fluxes and transport seen in our model, are consistent with modern Antarctic ice streams as well as the seemingly erratic behavior of paleo-ice streams during the last deglaciation.