  We show that addition of Metropolis single spin-flips to the Wolff cluster
flipping Monte Carlo procedure leads to a dramatic {\bf increase} in
performance for the spin-1/2 Ising model. We also show that adding Wolff
cluster flipping to the Metropolis or heat bath algorithms in systems where
just cluster flipping is not immediately obvious (such as the spin-3/2 Ising
model) can substantially {\bf reduce} the statistical errors of the
simulations. A further advantage of these methods is that systematic errors
introduced by the use of imperfect random number generation may be largely
healed by hybridizing single spin-flips with cluster flipping.
