Increased melting is often assumed to cause acceleration of ice sheets and glaciers through basal lubrication, possibly leading to increased rates of sea level rise. Now a physically-based model challenges this view, illustrating that above a critical threshold, increased melt will suppress the dynamic thinning process. Short-term spikes in water delivery, as from lake drainage or precipitation, still have the potential to generate spikes in velocity, but overall increases in melt do not appear likely to cause velocity increases.