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}, 2kgeq hgeq 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}, kgeq 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^2Lambda^3_{rm QCD}.
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