  The lasing threshold of a random laser is computed numerically from a generic
model. It is shown that spatial correlations of the disorder in the medium
(i.e., dielectric constant) lead to an increase of the decay rates of the
eigenmodes and of the lasing threshold. This is in conflict with predictions
that such correlations should lower the threshold. While all results are
derived for photonic systems, the computed decay rate distributions also apply
to electronic systems.
