We model the surface brightness profiles of a sample of 119 Abell Brightest Cluster Galaxies (BCG), finding a generalised deVaucouleurs R^{1/n} law, where n is a free parameter, to be appropriate. Departures from the R^{1/4} law are shown to be a real feature of galaxy profiles, not due to observational errors or coupling of n with the other model parameters. BCG typically have values of n greater than 4. The shape parameter n is shown to correlate with effective half-light radius, such that the larger BCG have larger values of n. This continues a trend noticed amongst ordinary elliptical galaxies and dwarf ellipticals, such that the fainter galaxies have smaller values of n.

To appear in Ap.J., 16 pages