Episodic debris fl ows scour the rock beds of many steepland valleys. Along recent debris-fl ow runout paths in the western United States, we have observed evidence for bedrock lowering, primarily by the impact of large particles entrained in debris fl ows. This evidence may persist to the point at which debris-fl ow deposition occurs, commonly at slopes of less than ~0.03-0.10. We fi nd that debris-fl ow-scoured valleys have a topographic signature that is fundamentally different from that predicted by bedrock river-incision models. Much of this difference results from the fact that local valley slope shows a tendency to decrease abruptly downstream of tributaries that contribute throughgoing debris fl ows. The degree of weathering of valley fl oor bedrock may also decrease abruptly downstream of such junctions. On the basis of these observations, we hypothesize that valley slope is adjusted to the long-term frequency of debris fl ows, and that valleys scoured by debris fl ows should not be modeled using conventional bedrock river-incision laws. We use fi eld observations to justify one possible debris-fl ow incision model, whose lowering rate is proportional to the integral of solid inertial normal stresses from particle impacts along the fl ow and the number of upvalley debris-fl ow sources. The model predicts that increases in incision rate caused by increases in fl ow event frequency and length (as fl ows gain material) downvalley are balanced by rate reductions from reduced inertial normal stress at lower slopes, and stronger, less weathered bedrock. These adjustments lead to a spatially uniform lowering rate. Although the proposed expression leads to equilibrium long-profi les with the correct topographic signature, the crudeness with which the debris-fl ow dynamics are parameterized reveals that we are far from a validated debris-fl ow incision law. However, the vast extent of steepland valley networks above slopes of ~0.03-0.10 illustrates the need to understand debris-fl ow incision if we hope to understand the evolution of steep topography around the world. Figure 1. Debris-fl ow valley network in an Oregon Coast Range clear-cut. The combination of elevated water pressure during a 1996 storm and reduced root strength initiated landslides at valley heads that mobilized as debris fl ows, scouring sediment and the Eocene Tyee sandstone (white areas) along the runout. Road at top right indicates scale.