This paper describes the FellWalker algorithm, a watershed algorithm that segments a 1-, 2- or 3-dimensional array of data values into a set of disjoint clumps of emission, each containing a single significant peak. Pixels below a nominated constant data level are assumed to be background pixels and are not assigned to any clump. FellWalker is thus equivalent in purpose to the CLUMPFIND algorithm. However, unlike CLUMPFIND, which segments the array on the basis of a set of evenly-spaced contours and thus uses only a small fraction of the available data values, the FellWalker algorithm is based on a gradient-tracing scheme which uses all available data values. Comparisons of CLUMPFIND and FellWalker using a crowded field of artificial Gaussian clumps, all of equal peak value and width, suggest that the results produced by FellWalker are less dependent on specific parameter settings than are those of CLUMPFIND.