Single-photon counting (SPC) x-ray imaging has the potential to improve image quality and enable new advanced energy-dependent methods. Recently, cascaded systems analysis (CSA) has been extended to the description of the detective quantum efficiency (DQE) of SPC detectors. In this article we apply the new CSA approach to the description of the DQE of hypothetical direct-conversion selenium (Sc) and cadmium zinc telluride (CdZnTc) detectors including the effects of poly-energetic x-ray spectra, stochastic conversion of x-ray energy to electron hole (c-h) pairs, depth-dependent collection of e-h pairs using the Hecht relation, additive electronic noise, and thresholding. Comparisons arc made to an energy-integrating model. For this simple model, with the exception of thick (1- 10 mm) Sc-bascd convertors, we found that the SPC DQE was 5-20 %greater than that of the energy integrating model. This trend was tnw even when additive noise was included in the SPC model and excluded from the energy-integrating model. However, the DQE of SPC detectors with poor collection efficiency (such as thick (<1 mm) Sc detectors) and high levels of additive noise can be degraded by 40-90 % for all energies and x-ray spectra considered. vVhile photon-counting approaches arc not yet ready for routine diagnostic imaging, the available DQE is equal to or higher than that of conventional energy-integrating detectors under a wide range of x-ray energies and convertor thickness. However, like energy-integrating detectors, the DQE of SPC detectors will be degraded by the combination of poor collection efficiency and high levels of additive noise.