A high-luminosity muon collider requires a reduction of the six-dimensional emittance of the captured muon beam by a factor of {approx} 10{sup 6}. Most of this cooling takes place in a dispersive channel that simultaneously reduces all six phase space dimensions. We describe a tapered 6D cooling channel that should meet the requirements of a muon collider. The parameters of the channel are given and preliminary simulations are shown of the expected performance. A complete scheme for cooling a muon beam sufficiently for use in a muon collider has been previously described. This scheme uses separate 6D ionization cooling channels for the two signs of the particle charge. In each, a channel first reduces the emittance of a train of muon bunches until they can be injected into a bunch-merging system. The single muon bunches, one of each sign, are then sent through a second tapered 6D cooling channel where the transverse emittance is reduced as much as possible and the longitudinal emittance is cooled to a value below that needed for the collider. The beam can then be recombined and sent through a final cooling channel using high-field solenoids that cools the transverse emittance to the required values for the collider while allowing the longitudinal emittance to grow. This paper mainly describes the design of the 6D cooling channel before bunch merging. Cooling efficiency is conveniently measured using a parameter Q, which is defined as the rate of change of 6D emittance divided by the rate of change of the number of muons in the beam. In a given lattice Q starts off small due to losses from initial matching, then rises to a large value (Q {approx} 15 is typical for the channels discussed here), and finally falls as the emittance of the beam approaches its equilibrium value. The idea for the 6D cooling channel described here originated with the RFOFO cooling ring. This design evolved into a helical channel referred to as a 'Guggenheim' in order to avoid serious problems with injection of large emittance beams. We found that good cooling efficiency requires that the channel be tapered. In that case when Q starts to fall off the lattice is modified to reduce the beta function. This ensures that the beam emittance is always large compared with the equilibrium emittance
