  We argue that bouncing branes occur naturally when there is more than one
extra-dimension. We consider three-branes embedded in space-times with a
horizon and an isometry group SO(6). As soon as the brane angular momentum is
large enough, a repulsive barrier prevents the branes from reaching the
horizon. We illustrate this phenomenon with the case of D3-branes in an
AdS_5-Schwarzschild-S_5 background and asymptotically flat space-time.
