At a given bulge luminosity (x-axis), galaxies have a range of velocity dispersion and size. Note that galaxies with high dispersion are also smaller -- they have deeper potentials.
Black hole mass correlates better with dispersion.
Black hole mass correlates even better with compactness (n = Sersic parameter).
The BH mass vs bulge relations also seem to apply to Active Galaxies -- where measurement of bulge velocity dispersion is more difficult.