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We are investigating a new cadmium zinc telluride (CZT) detector module with 0.5 mm3 reconstructed spatial resolution for small animal PET and plant imaging. Inter-pixel scatter will degrade the reconstructed spatial resolution and contrast resolution or, if the events are discarded, reduce the sensitivity. CZT also has poor time resolution leading to reduced contrast from random coincidences. We will use the kinematics of Compton scatter to estimate the position of inter-pixel scatter events so that these events can be used without degrading the spatial resolution. Further, we can estimate the incident photon direction from Compton kinematics to reject random coincidence photons. We evaluate the performance of our signal processing algorithms on a new split-layer design. The addition of Compton kinematics yielded up to a 50% improvement in contrast and CNR over processing without Compton kinematics.