  When analyzed in terms of the Symanzik expansion, lattice correlators of
multi-local (gauge-invariant) operators with non-trivial continuum limit
exhibit in maximally twisted lattice QCD ``infrared divergent'' cutoff effects
of the type a^{2k}/(m_\pi^2)^{h}, 2k\geq h\geq 1 (k,h integers), which tend to
become numerically large when the pion mass gets small. We prove that, if the
action is O(a) improved a` la Symanzik or, alternatively, the critical mass
counter-term is chosen in some ``optimal'' way, these lattice artifacts are
reduced to terms that are at worst of the order a^{2}(a^2/m_\pi^2)^{k-1}, k\geq
1. This implies that the continuum extrapolation of lattice results is smooth
at least down to values of the quark mass, m_q, satisfying the order of
magnitude inequality m_q >a^2\Lambda^3_{\rm QCD}.
