  We extend Wegner's exact solution for the 2D density of states at the lowest
Landau level with a short--range disorder to the cases of a double--layer
system and a superlattice. For the double--layer system, an analytical
expression for the density of states, illustrating the interplay between the
tunnel splitting of Landau levels and the disorder--induced broadening, is
obtained. For the superlattice, we derive an integral equation, the eigenvalue
of which determines the exact density of states. By solving this equation
numerically, we trace the disappearance of the miniband with increasing
disorder.
