Small animal PET scanners may be improved by increasing the sensitivity, improving the spatial resolution and improving the uniformity of the spatial resolution across the field of view. This may be achieved by using PET detectors based on crystal elements that are thin in the axial and transaxial directions and long in the radial direction, and by employing depth of interaction (DOI) encoding to minimize the parallax error. With DOI detectors, the diameter of the ring of the PET scanner may also be decreased. This minimizes the number of detectors required to achieve the same solid angle coverage as a scanner with a larger ring diameter and minimizes errors due to non-collinearity of the annihilation photons. In this study, we characterize prototype PET detectors that are finely pixelated with individual LSO crystal element sizes of 0.5 mm x 0.5 mm x 20 mm and 0.7 mm x 0.7 mm x 20 mm, read out at both ends by position sensitive avalanche photodiodes (PSAPDs). Both a specular reflector and a diffuse reflector were evaluated. The detectors were characterized based on the ability to clearly resolve the individual crystal elements, the DOI resolution and the energy resolution. Our results indicate that a scanner based on any of the four detector designs would offer improved spatial resolution and more uniform spatial resolution compared to present day small animal PET scanners. The greatest improvements to spatial resolution will be achieved when the detectors employing the 0.5 mm x 0.5 mm x 20 mm crystals are used. Monte Carlo simulations were performed to demonstrate that 2 mm DOI resolution is adequate to ensure uniform spatial resolution for a small animal PET scanner geometry using these detectors. The sensitivity of such a scanner was also simulated using Monte Carlo simulations and was shown to be greater than 10% for a four ring scanner with an inner diameter of 6 cm, employing 20 detectors per scanner ring.