  The Faddeev equations are solved in momentum space for the trinucleon bound
state with the new Tucson-Melbourne $\pi$ and $\rho$ exchange three-nucleon
potentials. The three-nucleon potentials are combined with a variety of
realistic two-nucleon potentials. The dependence of the triton binding energy
on the $\pi NN$ cut-off parameter in the three-nucleon potentials is studied
and found to be reduced compared to the case with pure $\pi$ exchange. The
$\rho$ exchange parts of the three-nucleon potential yield an overall repulsive
effect. When the recommended parameters are employed, the calculated triton
binding energy turns out to be very close to its experimental value.
Expectation values of various components of the three-nucleon potential are
given to illustrate their significance for binding.
