  We show that a shot noise free current at conductance below 2 e^2/h is
possible in short interacting quantum wires without spin-polarization. Our
calculation is done for two exactly solvable limits of the ``Coulomb Tonks
gas'', a one-dimensional gas of impenetrable electrons that can be realized in
ultra-thin quantum wires. In both cases we find that charge transport through
such a wire is noiseless at zero temperature while the conductance is reduced
to e^2/h.
