The land-terminating margin of the Greenland Ice Sheet has slowed down in recent decades, although the causes and implications for future ice flow are unclear. Explained originally by a self-regulating mechanism where basal slip reduces as drainage evolves from low to high efficiency, recent numerical modeling invokes a sedimentary control of ice sheet flow as an alternative hypothesis. Although both hypotheses can explain the recent slowdown, their respective forecasts of a long-term deceleration versus an acceleration of ice flow are contradictory. We present amplitude-versus-angle seismic data as the first observational test of the alternative hypothesis. We document transient modifications of basal sediment strengths by rapid subglacial drainages of supraglacial lakes, the primary current control on summer ice sheet flow according to our numerical model. Our observations agree with simulations of initial postdrainage sediment weakening and ice flow accelerations, and subsequent sediment restrengthening and ice flow decelerations, and thus confirm the alternative hypothesis. Although simulated melt season acceleration of ice flow due to weakening of subglacial sediments does not currently outweigh winter slowdown forced by self-regulation, they could dominate over the longer term. Subglacial sediments beneath the Greenland Ice Sheet must therefore be mapped and characterized, and a sedimentary control of ice flow must be evaluated against competing self-regulation mechanisms.