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An important challenge in positron emission tomography (PET) is the development of dedicated small-animal PET (muPET) systems having high sensitivity. In this paper, we investigate the use of an opposing pair of large-area detectors having high detection efficiency and moderate depth-of-interaction resolution in a compact scanner geometry for achieving a high system sensitivity. Substantial resolution degradations created by this hardware configuration, on the other hand, are corrected for by applying model-based image reconstruction. We have developed a prototype scanner adopting this design and evaluated its performance properties. Our results show that the prototype can achieve a central sensitivity of ~28.2% when using an energy window (EW) of 250-750 keV and a coincidence time window (CW) of 10 ns. When decreasing the EW to 400-750 keV, the central sensitivity still remains high at ~14.4%. Over the typical ranges of radioactivity used in PET rodent imaging with [18F]fluorodeoxyglucose (FDG), the prototype provides noise-equivalent count rates (NECRs) that are considerably higher than other muPET systems. For a mouse/rat-sized cylinder, we obtain a peak NECR of ~ 1.86/1.2 Mcps at ~32/40 MBq when using a 250/350-750 keV EW and a 6 ns CW. Using a resolution phantom, we obtain an average FWHM (full width at the half-maximum) of 1.79 mm for 1.35 mm-diameter rod sources when the axis of the phantom is vertical to the detectors of the prototype. This is consistent with the 1.2 mm FWHM image resolution previously obtained by using simulation data. The prototype also generates FDG rat images having good visual quality.