  We present high-resolution radio images at 1.4 GHz of two Galactic supernova
remnants (SNRs), G003.8--00.3 (formerly G003.7--00.2) and G350.0--02.0
(formerly G350.0-01.8). Although the two objects are very different in
appearance, in both cases the radio emission shows a clear bilateral (or
``barrel'') morphology for which the axis is parallel to the Galactic Plane.
  The majority of Galactic SNRs have now been observed at high resolution, and
one can define a clear bilateral subset of the population. We consider a sample
of 17 such SNRs, and find a highly significant tendency for the bilateral axes
of these SNRs to be aligned with the Galactic Plane. We interpret this as
indicating that ``extrinsic'' effects dominate the morphology of such remnants.
Specifically, we argue that the Galactic magnetic field causes these SNRs to
appear bilateral, either directly, in the form of magnetic field compression
and/or quasi-perpendicular acceleration of electrons in the supernova shock, or
more likely indirectly, by pre-processing the interstellar medium to produce
density stratifications extended along the Plane.
