  We propose various improvements of finite step-size updating for full QCD on
the lattice that might turn finite step-size updating into a viable alternative
to the hybrid Monte Carlo algorithm. These improvements are noise reduction of
the noisy estimator of the fermion determinant, unbiased inclusion of the
hopping parameter expansion and a multi-level Metropolis scheme. First
numerical tests are performed for the 2 dimensional Schwinger model with two
flavours of Wilson fermions and for QCD two flavours of Wilson fermions and
Schr"odinger functional boundary conditions.
