The measurement of depth of interaction (DOI) within detectors is necessary to improve resolution uniformity across the FOV of small diameter PET scanners. DOI encoding by pulse shape discrimination (PSD) has definite advantages as it requires only one readout per pixel and it allows DOI measurement of photoelectric and Compton events. The PSD time characteristics of various scintillators were studied with avalanche photodiodes (APD) and the identification capability was tested in multi-crystal assemblies with up to four scintillators. In the PSD time spectrum of an APD-GSO/LSO/BGO/CsI(TI) assembly, four distinct time peaks at 45, 26, 88 and 150 ns relative to a fast test pulse, having resolution of 10.6, 5.2, 20 and 27 ns, can be easily separated. Whereas the number and position of scintillators in the multi-crystal assemblies affect detector performance, the ability to identify crystals is not compromised. Compton events have a significant effect on PSD accuracy, suggesting that photopeak energy gating should be used for better crystal identification. However, more sophisticated PSD techniques using parametric time-energy histograms can also improve crystal identification in cases where PSD time or energy discrimination alone is inadequate. These results confirm the feasibility of PSD DOI encoding with APD-based detectors for PET.