  This paper examines the radiative transfer of synchrotron radiation in the
presence of a magnetic field configuration resulting from the compression of a
highly disordered magnetic field. It is shown that, provided Faraday rotation
and circular polarization can be neglected, the radiative transfer equations
for synchrotron radiation separate for this configuration, and the intensities
and polarization values for sources that are uniform on large scales can be
found straightforwardly in the case where opacity is significant. Although the
emission and absorption coefficients must, in general, be obtained numerically,
the process is much simpler than a full numerical solution to the transfer
equations. Some illustrative results are given and an interesting effect,
whereby the polarization increases while the magnetic field distribution
becomes less strongly confined to the plane of compression, is discussed.
  The results are of importance for the interpretation of polarization near the
edges of lobes in radio galaxies and of bright features in the parsec--scale
jets of AGN, where such magnetic field configurations are believed to exist.
  (Note: The original ApJ version of this paper contained two errata, which are
corrected in this version of the paper. First, Fig. 2 was plotted as a mirror
image of the correct version, reflected about the line $\log_{10}(\nu/
\nu_0)=0$. Second, as stated, Equation A16 is valid for $\gamma=2$, not
$\gamma=3$.)
