  Practical modifications of deterministic multigrid and conventional
relaxation algorithms are discussed. New parameters need not be tuned but are
determined by the algorithms themselves. One modification can be thought of as
``updating on a last layer consisting of a single site''. It eliminates
critical slowing down in computations of bosonic and fermionic propagators in a
fixed volume. Here critical slowing down means divergence of asymptotic
relaxation times as the propagators approach criticality. A remaining volume
dependence is weak enough in case of bosons so that conjugate gradient can be
outperformed. However, no answer can be given yet if the same is true for
staggered fermions on lattices of realizable sizes. Numerical results are
presented for propagators of bosons and of staggered fermions in 4-dimensional
$SU(2)$ gauge fields.
