  A high-energy muon collider scenario requires a "final cooling" system that
reduces transverse emittance by a factor of ~10 while allowing longitudinal
emittance increase. The baseline approach has low-energy transverse cooling
within high-field solenoids, with strong longitudinal heating. This approach
and its recent simulation are discussed. Alternative approaches which more
explicitly include emittance exchange are also presented. Round-to-flat beam
transform, transverse slicing, and longitudinal bunch coalescence are possible
components of the alternative approach. A more explicit understanding of
solenoidal cooling beam dynamics is introduced.
