The shape of submarine external channel levées has been assessed in a variety of systems, over a range of slope gradients, measuring both their thickness decay away from the parent channel and also the maximum gradient on the back-slope of the levée. The mathematical description of the shapes of the levées has been based on normalized data, using as characteristic length scales the distance from channel axis to the levée crest and the thickness of the entire levée (or levée package) at the levée crest. The variation in levée thickness perpendicular to the channel shows a clear pattern of power-law decay on steeper slopes (generally > 0·6°) and either exponential or logarithmic decay on gentler slopes. The levée shape is sensitive to local variations in slope and may change over only a few hundreds of metres in the flow direction. The threshold gradient between these two styles shows some variation and may be dependent on grain size. The maximum gradient on the back-slope of the levée shows a weak correlation with slope gradient, which varies from one system to another; this may also be a function of grain size. The variations in behaviour can be explained, in part, by differing rates of entrainment of ambient sea water into the currents as they flow over the levées, these rates being dependent upon the slope. Negligible entrainment on low gradients helps to explain the tendency to wider levées on low-gradient basin floors, as well as the persistence of channelized flows on low gradients, with little dissipation over extreme distances.