  We show that it is possible to improve the chiral behaviour and the approach
to the continuum limit of correlation functions in lattice QCD with Wilson
fermions by taking arithmetic averages of correlators computed in theories
regularized with Wilson terms of opposite sign. Improved hadronic masses and
matrix elements can be obtained by similarly averaging the corresponding
physical quantities separately computed within the two regularizations. To deal
with the problems related to the spectrum of the Wilson--Dirac operator, which
are particularly worrisome when Wilson and mass terms are such as to give
contributions of opposite sign to the real part of the eigenvalues, we propose
to use twisted-mass lattice QCD for the actual computation of the quantities
taking part to the averages. The choice $\pm \pi/2$ for the twisting angle is
particularly interesting, as O($a$) improved estimates of physical quantities
can be obtained even without averaging data from lattice formulations with
opposite Wilson terms. In all cases little or no extra computing power is
necessary, compared to simulations with standard Wilson fermions or
twisted-mass lattice QCD.
