The pulse height spectra from a new kind of unipolar gamma-ray detectors were predicted using a new three-dimensional simulation program developed at Sandia National Laboratories. The detectors were fabricated at Sandia and RMD Inc., and tested at Sandia. They were fabricated from Cd1-x.ZnxTe crystals and they were electron-transport-only devices. For the simulation, a successive overrelaxation method was used to determine the three-dimensional internal electric field within a detector, and to find the weighting potentials for the anode and the cathode. Uniform irradiation and ionization from a 137Cs source was assumed, and the charge transport and the signal induction within the detector were numerically computed using the appropriate materials and design parameters. The simulation gave excellent agreement with experimental pulse height spectra, and it demonstrated the power of such a simulation to correlate the materials parameters and the device design to the actual detector performance.