  Let $\calM_1$ and $\calM_2$ denote two compact hyperbolic manifolds. Assume
that the multiplicities of eigenvalues of the Laplacian acting on
$L^2(\calM_1)$ and $L^2(\calM_2)$ (respectively, multiplicities of lengths of
closed geodesics in $\calM_1$ and $\calM_2$) are the same, except for a
possibly infinite exceptional set of eigenvalues (respectively lengths). We
define a notion of density for the exceptional set and show that if it is below
a certain threshold, the two manifolds must be iso-spectral.
