Ice streams deposit sediment at their grounding lines, where ice reaches flotation. Grounding Zone Wedge (GZW) deposits indicate standstills in past grounding-line retreat, and are thought to stabilize grounding lines by reducing local water depth, restricting ice flow. However, the mechanisms of GZW growth are uncertain, as are the effects of sedimentation on a retreating grounding-line prior to GZW formation. We develop a 1-D coupled model of ice flow and sediment transport, considering both subglacial deposition of deforming sediments, and proglacial melt-out of entrained sediments from ice shelves. A refined grid near the grounding line resolves small sediment features and their effect on ice dynamics. The model simulates the growth of low-profile, prograding, asymmetric features consistent with observed GZWs. We find that the characteristic shape of GZWs arises from the coupling of sedimentation and ice dynamics. This mechanism is consistent with deposition from either deforming or entrained sediments, and does not require a low-profile ice shelf to limit vertical GZW growth. We also find that during grounding-line retreat, sedimentation provides a stabilizing feedback when other factors initially slow retreat. This may turn a slowdown in retreat into a long standstill, even when ice dynamics are far out of equilibrium. The feedback depends on total sediment flux and its spatial pattern of deposition, making these priorities for future study. Our study suggests that sedimentation might significantly extend pauses in deglaciation, and the model provides a new tool for exploring links between ice-stream dynamics and submarine landforms.