Comment on a universal upper bound on the entropy-to-energy ratio for bounded systems

Some difficulties are noted with Bekenstein's arguments that a system with energy $E$ and effective radius $R$ has an entropy bound $S\le S_B\equiv \frac{2\pi \mathrm{ER}}{\hslash c}$. The inequality appears to be valid only for large $S_B$. For that regime an upper bound which is generally stronger is proposed.