  We have obtained the best fit to the light profiles of a luminosity limited
sample of elliptical and S0 galaxies with a power law \rn, letting the exponent
remain free rather than keeping it fixed at $1/n=1/4$ as in the well known \GV
formula. The introduction of a free parameter in the fitting formula (ranging
from $n=0.5$ for $<\re>=0.3$ kpc to $n=16$ for $<\re>=25$ 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 consequence for the claimed
independence of the shape of galaxy profiles with respect to the Fundamental
Plane parameters.
