We discuss how the peculiar properties of maximally twisted Wilson fermions can be exploited to set up a consistent LQCD computational scheme in which the CP-conserving matrix elements of the ∆S = 1, 2 effective weak Hamiltonian can be evaluated without mixing with wrong-chirality and/or -parity operators. The proposed lattice framework guarantees automatic O(a) improvement and positive determinant also for pairs of non-degenerate quarks.