The Tucson-Melbourne two-pion exchange three-nucleon force is split into a reducible part mediated by Δ excitation and an irreducible part not mediated by Δ excitation. The triton binding energy is calculated. The irreducible part of the Tucson-Melbourne force is taken into account in the calculation. Its reducible part is discarded, but regenerated by the explicit treatment of the Δ isobar in a coupled-channel approach. The remaining irreducible part of the Tucson-Melbourne force makes a nonnegligible contribution to the triton binding energy. The strong dependence of the triton binding energy on the cutoff parameter for the πNN vertex in the Tucson-Melbourne force is considerably reduced
