A Bayesian method is described for reconstruction of high-resolution 3D images from the microPET small-animal scanner. Resolution recovery is achieved by explicitly modelling the depth dependent geometric sensitivity for each voxel in combination with an accurate detector response model that includes factors due to photon pair non-collinearity and inter-crystal scatter and penetration. To reduce storage and computational costs we use a factored matrix in which the detector response is modelled using a sinogram blurring kernel. Maximum a posteriori (MAP) images are reconstructed using this model in combination with a Poisson likelihood function and a Gibbs prior on the image. Reconstructions obtained from point source data using the accurate system model demonstrate a potential for near-isotropic FWHM resolution of approximately 1.2 mm at the center of the field of view compared with approximately 2 mm when using an analytic 3D reprojection (3DRP) method with a ramp filter. These results also show the ability of the accurate system model to compensate for resolution loss due to crystal penetration producing nearly constant radial FWHM resolution of 1 mm out to a 4 mm radius. Studies with a point source in a uniform cylinder indicate that as the resolution of the image is reduced to control noise propagation the resolution obtained using the accurate system model is superior to that obtained using 3DRP at matched background noise levels. Additional studies using pie phantoms with hot and cold cylinders of diameter 1-2.5 mm and 18FDG animal studies appear to confirm this observation.