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The position sensitivity in a 3”×3” LaBr3:Ce crystal has been simulated using collimated beams of medium and high energy γ-rays. The simulations have been done using the GEANT4 libraries which allow to follow both the gamma ray interaction in the detector and the scintillation light up to the photocathode. In the simulations the crystal has been coupled to an ideal PSPMT and/or a shielded PMT. The results indicate that in the 3” × 3” crystal with darkened surfaces it should be possible to localize the first interaction point of a 662 keV gamma ray within 1 cm, in the case of diffusive surfaces the position sensitivity deteriorates but it is not destroyed. As expected, the position sensitivity improves as the γ-ray energy increases. The measurements generally confirm the results given by simulations.