  We study conductance fluctuations in disordered quantum wires with unitary
symmetry focusing on the case in which the number of conducting channels in one
propagating direction is not equal to that in the opposite direction. We
consider disordered wires with $N+m$ left-moving channels and $N$ right-moving
channels. In this case, $m$ left-moving channels become perfectly conducting,
and the dimensionless conductance $g$ for the left-moving channels behaves as
$g \to m$ in the long-wire limit. We obtain the variance of $g$ in the
diffusive regime by using the Dorokhov-Mello-Pereyra-Kumar equation for
transmission eigenvalues. It is shown that the universality of conductance
fluctuations breaks down for $m \neq 0$ unless $N$ is very large.
