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Abstract Prior numerical modeling work has suggested that incision into sub‐horizontal layered stratigraphy with variable erodibility induces non‐uniform erosion rates even if base‐level fall is steady and sustained. Erosion rates of cliff bands formed in the stronger rocks in a stratigraphic sequence can greatly exceed the rate of base‐level fall. Where quartz in downstream sediment is sourced primarily from the stronger, cliff‐forming units, erosion rates estimated from concentrations of cosmogenic beryllium‐10 (¹⁰Be) in detrital sediment will reflect the locally high erosion rates in retreating cliff bands. We derive theoretical relationships for threshold hillslopes and channels described by the stream‐power incision model as a quantitative guide to the potential magnitude of this amplification of¹⁰Be‐derived erosion rates above the rate of base‐level fall. Our analyses predict that the degree of erosion rate amplification is a function of bedding dip and either the ratio of rock erodibility in alternating strong and weak layers in the channel network, or the ratio of cliff to intervening‐slope gradient on threshold hillslopes. We test our predictions in the cliff‐and‐bench landscape of the Grand Staircase in southern Utah, USA. We show that detrital cosmogenic erosion rates in this landscape are significantly higher (median 300 m/Ma) than the base‐level fall rate (~75 m/Ma) determined from the incision rate of a trunk stream into a ~0.6 Ma basalt flow emplaced along a 16 km reach of the channel. We infer a 3–6‐fold range in rock strength from near‐surface P‐wave velocity measurements. The approximately four‐fold difference between the median¹⁰Be‐derived erosion rate and the long‐term rate of base‐level fall is consistent with our model and the observation that the stronger, cliff‐forming lithologies in this landscape are the primary source of quartz in detrital sediments. © 2020 John Wiley & Sons, Ltd.