  For a conformally compact manifold that is hyperbolic near infinity and of
dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound
on the resonance counting function, correcting a mistake in the existing
literature. In the case of a compactly supported perturbation of a hyperbolic
manifold, we establish a Poisson formula expressing the regularized wave trace
as a sum over scattering resonances. This leads to an $r^{n+1}$ lower bound on
the counting function for scattering poles.
