  On geometrically finite hyperbolic manifolds $\Gamma\backslash H^{d}$,
including those with non-maximal rank cusps, we give upper bounds on the number
$N(R)$ of resonances of the Laplacian in disks of size $R$ as $R\to \infty$. In
particular, if the parabolic subgroups of $\Gamma$ satisfy a certain
Diophantine condition, the bound is $N(R)= O(R^d (\log R)^{d+1})$.
