It is often assumed that the maximum number of independent states a black hole may contain is $$N_{BH}=e^{BH}$$, where $$S_{BH} = A/4$$ is the Bekenstein-Hawking entropy and $$A$$ the horizon area in Planck units. I present a simple and straightforward argument showing that the number of states that can be distinguished by local observers inside the hole must be greater than this number.