  It is known that any minimal model M_p receives along its phi_31 irrelevant
direction *two* massless integrable flows: one from M_{p+1} perturbed by
phi_{13}, the other from Z_{p-1} parafermionic model perturbed by its
generating parafermion field. By comparing Thermodynamic Bethe Ansatz data and
``predictions'' of infrared Conformal Perturbation Theory we show that these
two flows are received by M_p with opposite coupling constants of the phi_31
irrelevant perturbation. Some comments on the massless S matrices of these two
flows are added.
