The surfaces of Earth and Mars contain large bedrock canyons that were carved by catastrophic outburst floods(1,2). Reconstructing the magnitude of these canyon-forming floods is essential for understanding the ways in which floods modify planetary surfaces(1,2), the hydrology of early Mars(3) and abrupt changes in climate(4). Flood discharges are often estimated by assuming that the floods filled the canyons to their brims with water; however, an alternative hypothesis is that canyon morphology adjusts during incision such that bed shear stresses exceed the threshold for erosion by a small amount(5). Here we show that accounting for erosion thresholds during canyon incision results in near-constant discharges that are five-to ten-fold smaller than full-to-the-brim estimates for Moses Coulee, a canyon in the Channeled Scablands, which was carved during the Pleistocene by the catastrophic Missoula floods in eastern Washington, USA. The predicted discharges are consistent with flow-depth indicators from gravel bars within the canyon. In contrast, under the assumption that floods filled canyons to their brims, a large and monotonic increase in flood discharge is predicted as the canyon was progressively incised, which is at odds with the discharges expected for floods originating from glacial lake outbursts. These findings suggest that flood-carved landscapes in fractured rock might evolve to a threshold state for bedrock erosion, thus implying much lower flood discharges than previously thought.