  In this paper we discuss how the peculiar properties of twisted lattice QCD
at maximal twist can be employed to set up a consistent computational scheme in
which, despite the explicit breaking of chiral symmetry induced by the presence
of the Wilson and mass terms in the action, it is possible to completely bypass
the problem of wrong chirality and parity mixings in the computation of the
CP-conserving matrix elements of the $\Delta S=1,2$ effective weak Hamiltonian
and at the same time have a positive determinant for non-degenerate quarks as
well as full O($a$) improvement in on-shell quantities with no need of
improving the lattice action and the operators.
