  In this work we consider the Anderson model on $\ell^2(\mathbb{Z}^d)$ when
the single site distribution (SSD) is given by $\mu_1 * \mu_2$, where $\mu_1$
is the Cauchy distribution and $\mu_2$ is any probability measure. For this
model we prove that the integrated density of states (IDS) is infinitely
differentiable irrespective of the disorder strength. Also, we investigate the
local eigenvalue statistics of this model in $d\ge 2$, without any assumption
on the localization property.
