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Denudation rate in unextended terranes is limited by the rate of bedrock channel incision, often modeled as work rate on the channel bed by water and sediment, or stream power. The latter can be generalized as KAmSn, where K represents the channel bed's resistance to lowering (whose variation with lithology is unknown), A is drainage area (a surrogate for discharge), S is local slope, and m and n are exponents whose values are debated. We address these uncertainties by simulating the lowering of ancient river profiles using the finite difference method. We vary m, n, and K to match the evolved profile as closely as possible to the corresponding modern river profile over a time period constrained by the age of the mapped paleoprofiles. We find at least two end-member incision laws, KA0.3–0.5S1 for Australian rivers with stable base levels and KfA0.1–0.2Sn for rivers in Kauai subject to abrupt base level change. The long-term lowering rate on the latter expression is a function of the frequency and magnitude of knickpoint erosion, characterized by Kf. Incision patterns from Japan and California could follow either expression. If they follow the first expression with m = 0.4, K varies from 10−7–10−6 m0.2/yr for granite and metamorphic rocks to 10−5–10−4 m0.2/yr for volcaniclastic rocks and 10−4–10−2 m0.2/yr for mudstones. This potentially large variation in K with lithology could drive strong variability in the rate of long-term landscape change, including denudation rate and sediment yield.