Growth of high-quality T1-doped p-type PbTe single crystals by Bridgman method under controlled Te or ph vapor pressure has been investigated. For high concentration of T1 in the melt (0.65 at%), the hole concentrations for crystals grown under applied Pb vapor pressures (1.5 x 10(19)-2 x 10(19)cm(-3)) are higher than those for crystals grown under applied Te vapor pressures (5 x 10(18)-8 x 10(18)cm(-3)). For low concentration of T1 (0.082 at%), the hole concentration is decreased with increasing Te vapor pressure. The PbTe crystals grown with high concentration of T1 under applied Pb vapor pressures show small FWHM of X-ray rocking curve ranging from 20 to 50 arcsec, Their etch pit densities are in the range of 8 x 10(4)-6 x 10(5) cm(-2), which are an order of magnitude lower than those of undoped PbTe crystals. These results indicate that highly T1-doped (0.65 at%) PbTe crystals, in particular, those grown under applied ph vapor pressure, have an excellent crystal quality.