  Polynomial approximations to the inverse of the fermion matrix are used to
filter the dynamics of the upper energy scales in HMC simulations. The use of a
multiple time-scale integration scheme allows the filtered pseudofermions to be
evolved using a coarse step size. We introduce a novel generalisation of the
nested leapfrog which allows for far greater flexibility in the choice of time
scales. We observe a reduction in the computational expense of the molecular
dynamics integration of between 3--5 which improves as the quark mass
decreases.
