Bedrock river incision occurs only during floods large enough to mobilize sediment and overcome substrate detachment thresholds. New data relating channel steepness and erosion rate provide the opportunity to evaluate the role of thresholds and discharge variability in landscape evolution. We augment an extensive erosion rate data set in the San Gabriel Mountains, California, with analysis of streamflow records and observations of channel width and sediment cover to evaluate the importance of climate and erosion thresholds on incision rates. We find the relationship between channel steepness and erosion rate in the San Gabriel Mountains can be explained using a simple stochastic-threshold incision model where the distribution of large floods follows an inverse power law, suggesting that details of incision mechanics, sediment effects, width adjustment, and debris flows do not significantly influence the steady state relationship between steepness and erosion rate. Using parameters tuned to this case, we vary climate parameters to explore a range of behavior for the steepness-erosion relationship. Erosion is enhanced by both increases in mean runoff and discharge variability. We explore the implications of an empirical relationship between mean runoff and variability to test whether dry, variable climates can erode more efficiently than wet, stable climates. For channels with high thresholds or low steepness, modeled erosion rate peaks at a mean runoff of 200–400 mm/yr. For much of the parameter space tested, erosion rates are predicted to be insensitive to increases in runoff above ∼500 mm/yr, with important implications for the hypothesized influence of climate on tectonics.