  Let $G$ be $\SO(n,1)$ or $\SU(n,1)$ and let $\Gamma\subset G$ denote an
arithmetic lattice. The hyperbolic manifold $\Gamma\backslash \calH$ comes with
a natural family of covers, coming from the congruence subgroups of $\Gamma$.
In many applications, it is useful to have a bound for the spectral gap that is
uniform for this family. When $\Gamma$ is itself a congruence lattice, there
are very good bounds coming from known results towards the Ramanujan
conjectures. In this paper, we establish an effective bound that is uniform for
congruence subgroups of a non-congruence lattice.
