We grew CdTexSe1−x (CTS) crystals from a Te-rich solution by using the traveling heater method (THM). The average size distribution and concentration of Te inclusions/precipitates in these as-grown samples were measured to be ~7×104 cm−3, which is much lower than values typical for the present state-of-the-art commercial CdZnTe (CZT) material. Their low-temperature photoluminescence measurement indicates high quality of the material; however the resistivity obtained via I–V curve measurements was ~5×108 Ω-cm, which is low in comparison to that required for gamma detectors. A well-resolved alpha response peak can be detected for both planar- and hemispherical detector geometry. The (μτ)e value for our as-grown sample at room temperature was found to be ~4×10−3 cm2/V.