  Motivated by questions of present interest in nuclear and condensed matter
physics we consider the superposition of a diagonal matrix with independent
random entries and a GUE. The relative strength of the two contributions is
determined by a parameter $\lambda$ suitably defined on the unfolded scale.
Using results for the spectral two-point correlator of this model obtained in
the framework of the supersymmetry method we focus attention on two different
regimes. For $\lambda$ << 1 the correlations are given by Dawson's integral
while for $\lambda$ >> 1 we derive a novel analytical formula for the two-point
function. In both cases the energy scales, in units of the mean level spacing,
at which deviations from pure GUE behavior become noticable can be identified.
We also derive an exact expansion of the local level density for finite level
number.
