A method is presented to improve the energy resolution of scintillators read out with Geiger-mode avalanche photodiode arrays. The method employs digital signal processing, in which individual decay curves for gamma-ray detection events are digitized and then fitted to analytical functions whose amplitude provides energy information. Simulation studies suggest that after-pulses represent the largest source of energy resolution loss, which can be improved with curve-fitting. An experimental measurement confirmed that energy resolution could be improved with least-square curve-fits to a simple exponential model.