  We report upper limits on the masses of black holes that can be present in
the centers of 16 nearby galaxy bulges. These limits for our statistically
complete sample were derived from the modeling of the central emission-line
widths ([N II] or [S II]), observed over a 0.25" X 0.2" (R < 9 pc) aperture.
The experiment has a mean detection sensitivity of 3.9 X 10^6 solar masses. For
three sample members with direct determinations of black hole masses our upper
limits agree within the uncertainties, while in general our upper limits are
found to be close to the masses measured in other bulges with global properties
similar to ours. Remarkably, our limits lie quite closely to the recently
derived relation between black hole mass and stellar velocity dispersion. These
results support a picture wherein the black hole mass and overall galaxy
structure are closely linked, as galaxies with exceptionally high black hole
masses at a given velocity dispersion apparently are rare.
