Compton cameras promise to improve the characteristics of nuclear medicine imaging, wherein mechanical collimation is replaced with electronic collimation. This leads to huge gains in sensitivity and, consequently, a reduction in the radiation dosage that needs to be administered to the patient. Design modifications that improve the sensitivity invariably compromise resolution. The scope of the current project was to determine an optimal design and configuration of a Compton camera that strikes a balance between these two properties. Transport of the photon flux from the source to the detectors was simulated with the camera geometry serving as the parameter to be optimized. Two variations of the Boltzmann photon transport equation, with and without photon polarization, were employed to model the flux. Doppler broadening of the energy spectra was also included. The simulation was done in a Monte Carlo framework using GEANT4. Two clinically relevant energies, 140 keV and 511 keV, corresponding to 99mTc and 18F were simulated. The gain in the sensitivity for the Compton camera over the conventional camera was 100 fold. Neither Doppler broadening nor polarization had any significant effect on the sensitivity of the camera. However, the spatial resolution of the camera was affected by these processes. Doppler broadening had a deleterious effect on the spatial resolution, but polarization improved the resolution when accounted for in the reconstruction algorithm.