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 >= h >= 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 >= 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 mq > a(2)Lambda(3)(QCD).