Methods for estimating palaeoslope from fluvial deposits have been available for some time, but new data and improved understanding of the relevant physical processes afford the possibility of improving existing methods, and the emerging field of quantitative stratigraphy provides a new context for the results. Here we focus on deriving palaeoslope estimates for coarse-grained fluvial deposits. These estimates can be used in basin analyses to constrain the magnitude of the slope change necessary for a given deflection of palaeocurrents, to constrain temporal and spatial variation in basin subsidence rate, and to provide a surface datum for use in sediment-backstripping calculations. The algorithm we derive to estimate palaeoslope applies to rivers that self-adjust through variations in channel width to maintain a temporally and spatially averaged bed shear stress equal to some constant multiple of the critical shear stress for initial motion of bed sediment. Data from modern coarse-grained rivers with minimal bank cohesion and form resistance suggest that this boundary shear stress is equal to about 1.4 times the critical shear stress for movement of the median-sized clast of the surface layer. The key sedimentological criteria for recognition of systems appropriate for this type of analysis are: (1) field relations suggesting that channel banks formed in effectively noncohesive gravel (i.e. free of clay-size sediment and plant roots); (2) absence of significant volumes of dune-derived cross-stratification; and (3) absence of indicators of extremely rapid, flash-flood-type deposition. The basic input data for a palaeoslope calculation are spatially averaged estimates of palaeodepth and median grain size. The most important aspect of data collection is that the depth and grain-size estimates should be determined independently by random sampling over the whole outcrop. Joint analysis of data from appropriate modern rivers and of errors associated with palaeodepth and grain-size estimates indicates that in coarse-grained braided-river deposits, palaeoslope can be estimated to within a factor of 2.