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The timing performance of a Compton PET device for very high resolution small animal imaging was investigated using Monte Carlo simulation data and timing simulations. The PET instrument was designed with an inner cylindrical silicon detector for scattering, surrounded by an outer cylindrical BGO scintillation detector for absorption. The time intervals between adjacent decay events of the annihilation photon source were extracted in accordance with the Poisson distribution for various source activities. Interaction time was estimated by adding the time of flight (TOF) obtained from Monte Carlo simulation data and timing uncertainty of the silicon and BGO detector to the decay time intervals. A Gaussian distribution (5 ns FWHM) and mono-exponential model (1.0 photoelectron/ns) were used for timing uncertainties of the silicon and BGO detectors, respectively. Maximizing the noise equivalent count rate (NECR) resulted in an energy window of of total energy sum and a timing window of 7 ns. Additional constraints imposed by the use of Compton kinematics information in this device proved valuable in rejecting random coincidences, object scatter and misclassified events. The improvement is most pronounced at high source activity.