New techniques for the crystal growth of Tl-based cuprate superconductors have been developed. It is found that a gold crucible and closed atmosphere are crucial for their crystal growth by a so-called self-flux method for a long time. As an example, crystals of Tl2Ba2CuOx, which is most important among the Tl-based cuprate superconductors because of its wide T-c-change and anomalous resistive critical fields, have been grown. Thus, mm-sized single crystals of Tl2Ba2CuOx in a high quality can be obtained. It should be noted that the value of the resistivity ratio R(300 K)/R(T-c) (RRR) of one of the as-grown crystals is 18.3. This high RRR value indicates that the newly developed techniques are useful to obtain extremely high-quality single crystals of not only Tl2Ba2CuOx but also other Tl-based cuprate superconductors,