  The identification of a causal-connection scale motivates us to propose a new
covariant bound on entropy within a generic space-like region. This "causal
entropy bound", scaling as the square root of EV, and thus lying around the
geometric mean of Bekenstein's S/ER and holographic S/A bounds, is checked in
various "critical" situations. In the case of limited gravity, Bekenstein's
bound is the strongest while naive holography is the weakest. In the case of
strong gravity, our bound and Bousso's holographic bound are stronger than
Bekenstein's, while naive holography is too tight, and hence typically wrong.
