  We explore the possibility of computing fermionic correlators on the lattice
by combining a domain decomposition with a multi-level integration scheme. The
quark propagator is expanded in series of terms with a well defined
hierarchical structure. The higher the order of a term, the (exponentially)
smaller its magnitude, the less local is its dependence on the gauge field.
Once inserted in a Wick contraction, the gauge-field dependence of the terms in
the resulting series can be factorized so that it is suitable for multi-level
Monte Carlo integration. We test the strategy in quenched QCD by computing the
disconnected correlator of two flavor-diagonal pseudoscalar densities, and a
nucleon two-point function. In either cases we observe a significant
exponential increase of the signal-to-noise ratio.
