  Practical ionization cooling rings could lead to lower cost or improved
performance in neutrino factory or muon collider designs. The ring modeled here
uses realistic three-dimensional fields. The performance of the ring compares
favorably with the linear cooling channel used in the second US Neutrino
Factory Study. The normalized 6D emittance of an ideal ring is decreased by a
factor of approximately 240, compared with a factor of only 15 for the linear
channel. We also examine such \textit{real-world} effects as windows on the
absorbers and rf cavities and leaving empty lattice cells for injection and
extraction. For realistic conditions the ring decreases the normalized 6D
emittance by a factor of 49.
