  A spherically symmetric spacetime is presented with an initial data set that
is asymptotically flat, satisfies the dominant energy condition, and such that
on this initial data $M<\sqrt{A/16\pi}$, where M is the total (ADM) mass and A
is the area of the apparent horizon. This provides a counterexample to a
commonly stated version of the Penrose inequality, though it does not
contradict the ``true'' Penrose inequality.
