A deconvolution methodology aimed to reduce the uncertainty for nondestructively predicting fuel burnup using gamma spectra collected with LaBr3 scintillators was developed. Deconvolution techniques have been used in the past to improve photopeak resolution of data collected using gamma detectors; however, they have not been used as a tool to more accurately predict fuel burnup. The deconvolution methodology consisted of calculating the detector response function using Monte Carlo simulations, validating the detector response function against experimental data, and implementing the maximum likelihood expectation maximization algorithm to enhance the LaBr3 gamma spectra. The deconvolution methodology was first tested on single-isotopic simulated data; later it was applied to fuel simulated data that were based on Advanced Test Reactor (ATR) fuel gamma spectra. The study showed that LaBr3 gamma spectra photopeak resolution and quality can be improved significantly using deconvolution methods, in addition to proving that enhancement techniques can be used to nondestructively predict ATR fuel burnup more accurately than using LaBr3 data without enhancements.