  The D-bound on the entropy of matter systems in de Sitter space is shown to
be closely related to the Bekenstein bound, which applies in a flat background.
This holds in arbitrary dimensions if the Bekenstein bound is calibrated by a
classical Geroch process. We discuss the relation of these bounds to the more
general bound on the entropy to area ratio. We find that black holes do not
saturate the Bekenstein bound in dimensions greater than four.
