  We prove that if $M \longrightarrow P$ is a small cover of a compact
right-angled hyperbolic polyhedron $P$ then $M$ admits a cofinal tower of
finite sheeted covers with positive rank gradient. As a corollary, if
$\pi_1(M)$ is commensurable with the reflection group of $P$, then $M$ admits a
cofinal tower of finite sheeted covers with positive rank gradient.
