We report the design of an optical floating-zone furnace for single-crystal growth under ultra-high vacuum (UHV) compatible conditions. The system is based on a commercial image furnace, which has been refurbished to be all-metal sealed. Major changes concern the use of UHV rotary feedthroughs and bespoke quartz-metal seals with metal-O-rings at the lamp stage. As a consequence, the procedure of assembling the furnace for crystal growth is changed completely. Bespoke heating jackets permit to bake the system. For compounds with elevated vapor pressures, the ultra-high vacuum serves as a precondition for the use of a high-purity argon atmosphere up to 10 bar. In the ferromagnetic Heusler compound Cu(2)MnAl, the improvements of purity result in an improved stability of the molten zone, grain selection, and, hence, single-crystal growth. Similar improvements are observed in traveling-solvent floating-zone growth of the antiferromagnetic Heusler compound Mn(3)Si. These improvements underscore the great potential of optical float-zoning for the growth of high-purity single crystals of intermetallic compounds.