We have obtained the best fit to the light profiles of a luminosity- limited sample of elliptical and S0 galaxies with a power law r^1/n^, letting the exponent remain free rather than keeping it fixed at 1/n = 1/4 as in the well-known de Vaucouleurs formula. The introduction of a free parameter in the fitting formula (ranging from n = 0.5 for (r_e_) = 0.3 kpc to n = 16 for (r_e_) = 25 kpc) is justified by the existence of a good correlation between n and the global galaxian parameters, such as total luminosity and scale-radius. This result seems to be in line with the segregation of properties between the `ordinary' and `bright' families of early-type galaxies, and has consequences for the claimed independence of the shape of galaxy profiles with respect to the Fundamental Plane parameters.