SSOR preconditioning of fermion matrix inversions which is parallelized usi
ng a locally-lexicographic lattice sub-division, has been shown to be very
efficient for standard Wilson fermions. We demonstrate here the power of th
is method for the Sheikholeslami-Wohlert improved fermion action and for a
renormalization group improved action incorporating couplings of the lattic
e fermion fields up to the diagonal in the unit hypercube.