  A high-energy muon collider scenario require 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 an alternative approach. Wedge-based emittance exchange could
provide much of the required transverse cooling with longitudinal heating.
Li-lens and quadrupole focusing systems could also provide much of the required
final cooling.
