  Using a new regulator, we examine 't Hooft's approach for evaluating black
hole entropy through a statistical-mechanical counting of states for a scalar
field propagating outside the event horizon. We find that this calculation
yields precisely the one-loop renormalization of the standard
Bekenstein-Hawking formula, $S={\Cal A}/(4G)$. Thus our result provides
evidence confirming a suggestion by Susskind and Uglum regarding black hole
entropy.
