  Collisionless shocks are frequently analyzed using the magnetohydrodynamics
(MHD) formalism, even though MHD assumes a small mean free path. Yet, isotropy
of pressure, fruit of binary collisions and assumed in MHD, may not apply in
collisionless shocks. This is especially true within a magnetized plasma, where
the field can stabilize an anisotropy.
  In a previous article \citep{BretJPP2022b}, a model was presented capable of
dealing with the anisotropies that may arise at the front crossing. It was
solved for any orientation of the field with respect to the shock front. Yet,
for some values of the upstream parameters, several downstream solutions were
found.
  Here, we complete the work started in \cite{BretJPP2022b} by showing how to
pick the physical solution out of the ones offered by the algebra. This is
achieved by 2 means: 1) selecting the solution that has the downstream field
obliquity closest to the upstream one. This criterion is exemplified on the
parallel case and backed up by Particle-in-Cell simulations. 2) Filtering out
solutions which do not satisfy a criteria already invoked to trim multiple
solutions in MHD: the evolutionarity criterion, that we assume valid in the
collisionless case.
  The end result is a model in which a given upstream configuration results in
a unique, or none (like in MHD), downstream configuration. The largest
departure from MHD is found for the case of a parallel shock.
