  Previous work has shown that high-quality control variates for lattice Monte
Carlo methods may be constructed from lattice Schwinger-Dyson relations. This
paper extends that method to theories with lattice fermions, using the Thirring
model in $1+1$ spacetime dimensions as a testbed. Past construction of these
control variates involved a number of fitting parameters that scaled with
lattice volume. By computing the control variate in perturbation theory, the
number of fitting parameters required for an order-of-magnitude improvement in
the signal-to-noise ratio at weak coupling is reduced to be of order one.
