Sediment fans are a potentially useful and underexploited recorder of Earth's climatic and tectonic history, but historical observations have led to conflicting views on the importance of tectonic, climatic, and lithologic variables in controlling fan morphology and deposition. A one-dimensional model of a sediment fan and its associated catchment is used to explore the sensitivity of such simple sediment routing systems to perturbations in fault slip and precipitation rates. A transport-limited catchment is coupled to a fan whose surface slope is set by the balance between catchment sediment efflux and the available tectonically generated basin accommodation. Rock uplift rate is spatially variable across the model space. Increasing the fault slip rate, or decreasing the precipitation rate, leads to an increase in fan slope, temporary back-stepping of the fan toe, and a pronounced angular unconformity. Conversely, a decrease in slip rate, or an increase in precipitation rate, results in a decrease in fan slope, and progradation and eventual stabilization of the fan toe. Once perturbed, the system evolves toward a new equilibrium state with time constants of ∼0.5 to 2 Myr; these response times are insensitive to slip rate but are strongly dependent on precipitation rate. Variations in fan slope are well described by a dimensionless parameter that expresses equilibrium slope as a function of slip rate, precipitation rate, system size, and catchment lithology. This parameter holds promise as a predictive tool in inverting the morphology of natural fans for environmental variables.