  We present a new method for reducing the stochastic noise of all-to-all
propagators based on stopping the inversion of the propagator before
convergence. The method is easy to implement, unbiased and independent of the
quark action. Applying this method to the calculation of disconnected loops
needed for hadronic structure observables we find savings in computer time of
factors of 4-12 depending on the operator inserted in the loop. When combined
with a hopping parameter expansion technique we obtain combined gains of up to
factors of 30 for some operators.
