Accurately specifying the relationship between basal drag on a hard, rough glacier bed and sliding speed is a long-standing and central challenge in glaciology. Drag on a rigid bed consisting of steps with linear treads inclined upglacier—a good idealization for the bedrock morphology of some hard-bedded glaciers—has been considered in sliding theories but never studied empirically. Balancing forces parallel to step treads indicates that drag should be independent of sliding speed and cavity size and set by the limit-equilibrium condition sometimes called Iken's bound. In this study we used a large ring-shear device to slide ice at its pressure melting temperature across a stepped bed, over a range of steady sliding speeds (29–348 m yr−1), and under a steady effective pressure (500 kPa). Contrary to expectation, drag decreased 42% with increasing sliding speed and cavity size. Experimental deviations from theory cannot explain this decrease in drag with increasing sliding speed (i.e., rate weakening). We suggest that stress bridging in ice between ice-bed contact zones and cavities causes stress gradients that require viscous deformation of ice to sustain stress equilibrium, so that contact zones can be at shear stresses below limit-equilibrium values. A parameter—linearly dependent on sliding speed—that scales the extent of ice deformation to areas of ice-bed contact allows the experimental drag relationship to be fitted with a simple sliding model. Rate-weakening drag has now been observed for two contrasting bed morphologies, stepped and sinusoidal, highlighting the need to consider such behavior in glacier flow models.