  In this note, we study Lifshitz tails for a 2D Landau Hamiltonian perturbed
by a random alloy-type potential constructed with single site potentials
decaying at least at a Gaussian speed. We prove that, if the Landau level stays
preserved as a band edge for the perturbed Hamiltonian, at the Landau levels,
the integrated density of states has a Lifshitz behavior of the type
$e^{-\log^2|E-2bq|}$.
