  We investigate in detail a 2-level algorithm for the computation of 2-point
functions of fuzzy Wilson loops in lattice gauge theory. Its performance and
the optimization of its parameters are described in the context of 2+1D SU(2)
gluodynamics. In realistic calculations of glueball masses, it is found that
the reduction in CPU time for given error bars on the correlator at
time-separation ~0.2fm, where a mass-plateau sets in, varies between 1.5 and 7
for the lightest glueballs in the non-trivial symmetry channels; only for the
lightest glueball is the 2-level algorithm not helpful. For the heavier states,
or for larger time-separations, the gain increases as expected exponentially in
(mt). We present further physics applications in 2+1 and 3+1 dimensions and for
different gauge groups that confirm these conclusions.
