The incision of rivers in bedrock is thought to be an important factor that influences the evolution of relief in tectonically active orogens. At present, there are at least six competing models for incision of bedrock rivers, but these models have received little quantitative testing. We statistically evaluate these models using observations from the Clearwater River in northwestern Washington State, which crosses the actively rising forearc high of the Cascadia margin. A previous study has used fluvial terraces along the Clearwater to estimate bedrock incision rates over the last ~150 kyr. They show that incision rates have been steady over the long-term (>50 kyr), consistent with other evidence based on isotopic cooling ages, for steady long-term (>1 Myr) erosion rates. The steady state character of the river allows us to use the relatively simple time-invariant solutions for the various incision models and also to estimate long-term sediment discharge along the river, which is a critical variable for some incision models. An interesting feature of the Clearwater River is that it has a downstream decrease in the rate of incision, from ~0.9 mm/yr in the headwater to <0.1 mm/yr at the coast. None of the incision models, including the shear stress model, successfully accounts for this relationship. This result may be due to the simple way in which these models are used, commonly without consideration for the distribution of discharge with time, and the variable capacity of the river channel to contain peak flows along its course. We suggest some general improvements for the incision models, and also guidelines for selecting those rivers that will allow good discrimination between competing models.