Single crystals of CdTe-based quaternary alloys are grown by a vertical Bridgman method. The lattice constant of the quaternary ingot is proposed to match that of Cd0.8Zn0.2Te. To compensate the Zn segregation in CdTe, a suitable amount of Se or S was added along with Zn. We found that the compensate effect was not significant, particularly for the CdZnTeS alloy. Nevertheless, an ingot with a fairly uniform lattice constant was obtained for the CdZnTeSe alloy mainly because the effective segregation coefficient of Se was close to one. A study using double crystal X-ray diffractometry indicated that the addition of Se or S to CdZnTe would degrade the crystal quality.