  Channel symmetry properties that imply the tightness of Shannon's random
coding inner bound have recently been used to determine the capacity region of
discrete-memoryless two-way channels (DM-TWCs). For channels without such
symmetry properties, outer bounds are often needed to estimate the capacity
region. However, validating symmetry conditions and/or evaluating non-trivial
outer bounds are computationally demanding, especially for channels with large
input and output alphabets. In this paper, three easy-to-check conditions that
identify DM-TWCs with no such symmetry properties as well as an easy-to-compute
outer bound are derived. The bound is obtained from Shannon's inner bound
computation but is non-trivial. Using this outer bound, approximate capacity
results can be established for certain DM-TWCs. The results are illustrated by
two examples.
