Bedrock rivers are the mediators of environmental change through mountainous landscapes. In response to an increase in uplift rate for example, a “knickpoint” (often materialised as a waterfall) will propagate upstream, separating a domain downstream where the river and its adjacent hillslopes have steepened in response to the change from a “relict” domain upstream which is adjusted to the conditions before the change (Crosby and Whipple 2006). Many studies assume that knickpoint propagation rate scales with drainage area, based on the stream power theory. However, recent studies in a range of locations have found no obvious relationship between knickpoint retreat rate and drainage area, potentially resulting from the stream power law neglecting (i) the influence of sediment on the processes associated with waterfall migration and (ii) thresholds for bedrock detachment (Cook et al. 2013; Mackey et al. 2014; DiBiase et al. 2015; Baynes et al. 2015; Brocard et al. 2016). In this study, we develop a 1D model of waterfall retreat in horizontally bedded bedrock with varying joint spacing. In the model, knickpoint migration is based on two rules: a waterfall will start migrating once the threshold flow depth (a function of knickpoint height and joint spacing) has been exceeded (Lamb and Dietrich 2009), and the migration rate will then be a function of the water-depth-to-waterfall-height ratio, based on experimental results by Baynes (2015). Using a hydrograph based on a Poisson rectangular pulse rainfall simulator (Tucker and Bras 2001), we demonstrate the importance of structure in controlling the speed at which waterfalls migrate but also their number and the length over which they are distributed (Fig. 1). The model is applied to the Jökulsá á Fjöllum, NE Iceland, where rapid migration of waterfalls as a result of discrete events has been identified (Baynes et al. 2015), using new constraints on joint spacing derived from high resolution lidar survey of the gorge walls.