  We investigate the Brillouin action in terms of its suitability as a kernel
to the overlap procedure, with a view on both heavy and light quark physics. We
use the diagonal elements of the Kenney-Laub family of iterations for the
sparse matrix sign function, since they grow monotonically and facilitate
cascaded preconditioning strategies with different rational approximations to
the sign function. We find that the overlap action with the Brillouin kernel is
significantly better localized than the version with the Wilson kernel.
