Self-similar downstream grain-size fining trends in fluvial deposits are being increasingly used to simplify equilibrium sediment transport dynamics in numerical models. Their ability to collapse time-averaged behavior of a depositional system into a simple mass balance framework makes them ideal for exploring the sensitivity of sediment routing systems to their climatic and tectonic boundary conditions. This is important if we want to better understand the sensitivity of landscapes to environmental change over timescales >10 2 years. However, the extent to which self-similarity is detectable in the deposits of natural rivers is not fully constrained. In transport-limited rivers, stored sediment can be remobilized or "recycled" and this behavior has been highlighted as a mechanism by which externally forced grain-size fining trends are distorted. Here we evaluate evidence of self-similarity in surface gravel-size distributions on three geomorphically diverse alluvial fans in the Iglesia basin, south Central Argentine Andes. We find that size distributions are self-similar, deviating from that condition only when significant variability occurs in the coarse tails of the distributions. Our analysis indicates a strong correlation between the degree of sediment recycling and the proportion of coarse clasts present on the bed surface. However, by fitting a relative mobility transfer function, we demonstrate that size-selectivity alone can explain the bulk size distributions observed. This strengthens the application of self-similar grain size fining models to solving problems of mass balance in a range of geomorphic settings, with an aim for reconstructing environmental boundary conditions from stratigraphy.Plain Language Summary To date, little research has been conducted into how sensitively rivers respond to changes in their sediment and water supplies. This is because river processes that control how and when sediment moves are complex and evolve in response to landscape change over a wide range of time and spatial scales. Using a unique field site in the Argentine Andes, we find evidence for an important river behavior that can simplify the complexity of physical river processes in space and time. Each of three rivers investigated had sorted the gravel they transport by size, both locally on the river bed and along their downstream length. We found that at any site along the river, the degree to which the gravel is sorted is the same. This means that taking into account the change in sediment size downstream, the underlying grain size distributions are all the same. As size sorting is related to the efficiency of the river to transport its sediment load, we can use this finding to reconstruct the mobility of sediment anywhere along the river. We do this by fitting a simple and elegant transfer function to our data, which can be incorporated into models of long-term river evolution.