Glaciological theory predicts that the subglacial drainage network at the base of gently sloping ice sheets resting on deforming sediment should consist of many wide, shallow, probably braided "canals" distributed along the ice-sediment interface, rather than an arborescent network of relatively few large tunnels, as would develop over a rigid substrate. A corollary prediction examined here is that eskers, which form in large subglacial tunnels, should be rare where subglacial bed deformation occurred, but they may be relatively common where the bed was rigid. Bed deformation would be most likely where subglacial till was relatively continuous, fine-grained, and of low permeability—that is, in regions where till is derived primarily from underlying sedimentary bedrock—but unlikely where discontinuous, coarse-grained, high-permeability till was derived from underlying crystalline bedrock. The observed distribution of eskers in areas covered by the Laurentide and Eurasian (British, Scandinavian, and Barents Sea) ice sheets during the last glaciation shows that most eskers occur over crystalline bedrock overlain by discontinuous, high-permeability till, but are rare or absent over sedimentary bedrock overlain by fine-grained, low-permeability till, thus matching reasonably well our prediction. Glaciological theory and geologic evidence indicate that esker systems on a subcontinental scale are time-transgressive. Sedimentological evidence for a "canal" drainage system appears to be present in fine-grained tills where eskers are largely absent.