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Improved spatial resolution without sacrificing sensitivity is one of the most challenging developmental goals for small animal PET scanners. The 3-layer configuration that we propose here utilizes relative offsets of half a crystal pitch in x- and y-directions, and pulse shape discrimination to obtain depth of interaction (DOI). Three layers of crystals with a dimension 1.5 x 1.5 x 7.0 mm3 were composed of a L0.2 GSO (Lu0.4 Gd1.6 SiO4: Ce) crystal layer and a L0.9 GSO (Lu1.8 Gd0.2 SiO4 Ce) crystal layer aligned with each other, and a L0.9 GSO crystal layer offset at half a crystal pitch in x- and y-directions. The L0.9 GSO crystal layer was attached to a Hamamatsu H9500 flat-panel PMT. The devised small animal PET scanner has a diameter of 84 mm with one detector ring, and can be upgraded to two detector rings. GEANT4 Monte-Carlo simulation was used to estimate sensitivities of ~12% and ~20%, respectively, at the center of one and two PMT ring system with an energy window of 350~750 keV. We present flood images with peak-to-valley ratios of about 5-6 obtained using 22Na and layer identification capability of ~99 % with pulse shape analysis, and verified the basic concepts of multi-layer small animal PET.