In steepland valleys subject to debris flows, episodic deposition typically inundates valley bottoms, but channels nevertheless incise deposits and erode bedrock. The hypothesis explored here is that, while continual fluvial processes evacuate deposits, temporary storage of episodic deposition drives creation of accommodation space through valley width adjustment. Data from three headwater valleys in the Oregon Coast Range show that, where valley width is variable and increases downstream, average valley bottom deposit depth is similar among sites and stationary with respect to contributing area. A simple numerical model of valley cross section evolution couples continual soil production and nonlinear diffusion, constant but contrasting rates of channel incision into deposits and bedrock, and episodic valley bottom-inundating deposition. The model reproduces observed features including flat, deposit-covered valley bottoms and abrupt transitions to steep (often oversteepened) valley sides. Simulations address sensitivity to two dimensionless numbers: (1) transverse slope number describes relative amplitudes of random transverse slopes of deposits and random white noise added to deposit surfaces; and (2) deposition number describes deposition rate relative to evacuation. Simulated valley bottom width increases with deposition and is maximum for deposition number near unity, but as in the data, simulated deposit depth is nearly constant over a large part of the parameter space. Field data and simulation results imply that valley width adjustment is the primary landscape response to changing sediment supply: while valley profile steepening is limited by rock uplift rate, valley widening is limited by the bedrock incision rate and is therefore potentially faster.