Resistance at the ice-bed interface provides a strong control on the response of ice streams and outlet glaciers to external forcing, yet it is not observable by remote sensing. We used inverse methods constrained by satellite observations to infer the basal resistance to flow underneath three of the Greenland Ice Sheet's largest outlet glaciers. In regions of fast ice flow and high (>250 kPa) driving stresses, ice is often assumed to flow over a strong bed. We found, however, that the beds of these three glaciers provide almost no resistance under the fast-flowing trunk. Instead, resistance to flow is provided by the lateral margins and stronger beds underlying slower-moving ice upstream. Additionally, we found isolated patches of high basal resistivity within the predominantly weak beds. Because these small-scale (<1 ice thickness) features may be artifacts of overfitting our solution to measurement errors, we tested their robustness to different degrees of regularization.