This study investigates the effect of energy threshold on being able to include and position multiple-interaction photon events (MIPEs) detected in a cadmium zinc telluride (CZT) based small animal PET system we have built. Due to noise fluctuations, each channel's data acquisition trigger threshold should be adjusted above the noise floor, which limits the detection of photon interactions with energy below the threshold. If not identified, these events will lead to a loss of photon sensitivity as well as reconstructed image spatial resolution and/or contrast. GATE simulations with a cylinder having four hot rods were carried out and it was shown that for an energy threshold of 50 keV and above, at least 14% of events will be mispositioned due to the loss of first and/or second interaction in MIPEs. Compton kinematics is leveraged to mitigate this problem by classifying mispositioned trues, in addition to random and (phantom) scatter events through the use of a novel 'angular threshold' which maximizes a figure of merit inspired by noise equivalent counts. An angular threshold of 3° was found to detect 63% of mispositioned MIPEs, along with 80% of randoms and 66% of scatters with system energy resolution of 7.4% FWHM and system time resolution of 30 ns FWHM. The simulation results will be used to guide data processing of experimental phantom results.