  Applying domain decomposition to the lattice Dirac operator and the
associated quark propagator, we arrive at expressions which, with the proper
insertion of random sources therein, can provide improvement to the estimation
of the propagator. Schemes are considered for both open and closed (or loop)
propagators. In the end, our technique for improving open contributions is
similar to the ``maximal variance reduction'' approach of Michael and Peisa,
but contains the advantage, especially for improved actions, of dealing
directly with the Dirac operator. Using these improved open propagators for the
Chirally Improved operator, we present preliminary results for the static-light
meson spectrum.
