  Transport properties of a single-channel Luttinger liquid impinging on a
barrier have been studied for $g=1/2 - \epsilon$, where $g$ is the
dimensionless interaction constant and $|\epsilon| \ll 1$. The relevant
diagrams contributing to the conductance are identified and evaluated in all
orders. Our approach represents a leading-log summation which is valid for
sufficiently low temperature and small voltage. The asymptotic low-temperature
corrections exhibit a turnover from the $T^{2/g-2}$ behavior to a universal
$T^2$ law as the voltage is increased.
