The identification of a causal-connection scale motivates us to propose a n
ew covariant bound on entropy within a generic spacelike region; This "caus
al entropy bound," scaling as root EV, and;thus lying around the geometric
mean of Bekenstein's S/ER and holographic SIA 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 stro
ng gravity, our bound and Bousso's holographic bound are stronger than Beke
nstein's, while naive holography is too tight, and hence typically wrong.