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Progress on six dimensional ionization muon cooling with relatively smallrings of magnets is described. Lattices being explored include scaling sectorcyclotrons with edge focusing and strong focusing, fixed field alternatinggradient (FFAG) rings. Ionization cooling is provided by high pressure hydrogengas which removes both transverse and longitudinal momentum. Lost longitudinalmomentum is replaced using radio frequency (RF) cavities, giving a nettransverse emittance reduction. The longer path length in the hydrogen ofhigher momentum muons decreases longitudinal emittance at the expense oftransverse emittance. Thus emittance exchange allows these rings to cool in allsix dimensions and not just transversely. Alternatively, if the RF is locatedafter the ring, it may be possible to cool the muons by stopping them as theyspiral adiabatically into a central swarm. As momentum goes to zero, themomentum spread goes to zero. The resulting cooled muons can lead to an intensemuon beam which could be a source for neutrino factories or muon colliders.Comment: Six pages. One LaTeX, one style, and five postscript figure files. To  appear in the proceedings of DPF 2004: Annual Meeting of the Division of  Particles and Fields (DPF) of the American Physical Society (APS), Riverside,  California, 26-31 Aug 200

6D IONIZATION MUON COOLING WITH TABLETOP RINGS