A critical element in the Time Dependent Processing chain for scanning infrared sensors is electronic gamma circumvention. The most successful approach to gamma circumvention to date is a two stage algorithm, Spike Adaptive Time Delay and Integration (SATDI). This heuristic approach makes no assumptions about gamma-induced noise except that it is an additive corruption of the true signal. If, however, one can model the form of the gamma-induced noise distribution, it is possible to design a maximum likelihood estimation model which explicitly utilizes the parametric form of the noise. Such a model will, in general, be more efficient than a heuristic one, since it contains more information about the noise process. The parametric form studied in this paper is an exponential distribution, λe-λr, where r is the received signal. This distribution is a reasonable approximation to the observed gamma spectrum in infrared detectors. A maximum likelihood estimation equation corresponding to this noise distribution is derived, and its performance is compared to SATDI. It is found that, for a bright gamma background, either much better detection for a fixed false alarm rate, or many fewer false alarms for a fixed detection probability, may be achieved using the maximum likelihood estimator as compared to SATDI.