Statistical Interpretation of the Bekenstein Entropy for Systems with a Stretched Horizon

For the two-charge extremal holes in string theory we show that the Bekenstein entropy obtained from the area of the stretched horizon has a statistical interpretation as a ``coarse graining entropy'': different microstates give geometries that differ near r0ex{0ex}=0ex{0ex}0, and the stretched horizon cuts off the metric at r0ex{0ex}=0ex{0ex}b where these geometries start to differ.