We make large (in excess of 2 cm in diameter), single crystal YBa.sub.2 Cu.sub.3 O.sub.7-x [123 YBCO] crystals, where x.ltoreq.0.6, in a seventeen step process or some variant thereof from finely ground and well mixed 123 YBCO and 211 YBCO powders with a small amount of Pt by controlling the rate of cooling from within a compact of the powders using a temperature gradient in the radial and axial planes (independently) of about 1-1.degree. C./inch diameter of compact to nucleate the crystal growth. We promote crystal growth as well using a samarium oxide seed crystal, preferably SmBa.sub.2 Cu.sub.3 O.sub.(7-y), where y.ltoreq.1.6. After nucleation we cool the compact slowly at a rate from about 0.1-1.degree. C./hr to promote the single crystal development.