  We study the conductance of disordered wires with unitary symmetry focusing
on the case in which $m$ perfectly conducting channels are present due to the
channel-number imbalance between two-propagating directions. Using the exact
solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission
eigenvalues, we obtain the average and second moment of the conductance in the
long-wire regime. For comparison, we employ the three-edge Chalker-Coddington
model as the simplest example of channel-number-imbalanced systems with $m =
1$, and obtain the average and second moment of the conductance by using a
supersymmetry approach. We show that the result for the Chalker-Coddington
model is identical to that obtained from the DMPK equation.
