  We rederive the universal bound on entropy with the help of black holes while
allowing for Unruh--Wald buoyancy. We consider a box full of entropy lowered
towards and then dropped into a Reissner--Nordstr\"om black hole in equilibrium
with thermal radiation. We avoid the approximation that the buoyant pressure
varies slowly across the box, and compute the buoyant force exactly. We find,
in agreement with independent investigations, that the neutral point
generically lies very near the horizon. A consequence is that in the generic
case, the Unruh--Wald entropy restriction is neither necessary nor sufficient
for enforcement of the generalized second law. Another consequence is that
generically the buoyancy makes only a negligible contribution to the energy
bookeeping, so that the original entropy bound is recovered if the generalized
second law is assumed to hold. The number of particle species does not figure
in the entropy bound, a point that has caused some perplexity. We demonstrate
by explicit calculation that, for arbitrarily large number of particle species,
the bound is indeed satisfied by cavity thermal radiation in the thermodynamic
regime, provided vacuum energies are included. We also show directly that
thermal radiation in a cavity in $D$ dimensional space also respects the bound
regardless of the value of $D$. As an application of the bound we show that it
strongly restricts the information capacity of the posited black hole remnants,
so that they cannot serve to resolve the information paradox.
