  We study the Anderson localization of atomic gases exposed to
three-dimensional optical speckles by analyzing the statistics of the
energy-level spacings. This method allows us to consider realistic models of
the speckle patterns, taking into account the strongly anisotropic correlations
which are realized in concrete experimental configurations. We first compute
the mobility edge $E_c$ of a speckle pattern created using a single laser beam.
We find that $E_c$ drifts when we vary the anisotropy of the speckle grains,
going from higher values when the speckles are squeezed along the beam
propagation axis, to lower values when they are elongated. We also consider the
case where two speckle patterns are superimposed forming interference fringes,
and we find that $E_c$ is increased compared to the case of idealized isotropic
disorder. We discuss the important implications of our findings for cold-atoms
experiments.
