We have investigated the effect of incorporation of Se into CdZnTe (CZT) matrix on x-ray response of single crystal direct conversion detectors. We used horizontal Bridgman technique for crystal growth. We have characterized the crystals using an array of diagnostics including photo-induced current transient spectroscopy (PICTS), electric field distribution using Pockels effect, and count rate response to high flux incident x-ray irradiation. We have demonstrated that the density of deep-level traps was significantly reduced by the addition of Se, resulting in more uniform electric field inside the crystal and an associated increase in x-ray count rate. The inclusion of Se within the CZT matrix, combined with additional optimization of the growth recipe enabled linear response at high incident x-ray flux.