Distributions of scour and fill depths recorded in three low-order sand bed dryland rivers were compared with the Weibull, gamma, exponential, and lognormal probability density functions to determine which model best describes the reach-scale variability in scour and fill. Goodness of fit tests confirm that the majority of scour distributions conform to the one-parameter exponential model at the 95% significance level. The positive relationship between exponential model parameters and flow strength provides a means to estimate streambed scour depths, at least to a first approximation, in comparable streams. In contrast, the majority of the fill distributions do not conform to the exponential model even though depths of scour and fill are broadly similar. The disparities between the distributions of scour and fill raise questions about notions of channel equilibrium and about the role of scour and fill in effecting channel change.