A way to improve the spatial resolution in positron emission tomography (PET) is to determine the depth-of-interaction (DOI) in the detector. A way to achieve this is to use the phoswich approach, a detector with two or more layers of different scintitlators. The layer identification is done by using differences in scintillation decay time and pulse shape discrimination techniques. The advantages of the concept have been demonstrated in the HRRT high resolution PET system using a LSO/LYSO combination giving a high spatial resolution uniformity of around 2.5 mm within a larger part of the imaged volume. A phoswich combination that lately has received attention is LuAP/LSO or LuYAP/LSO. The suggestions come from the Crystal Clear Collaboration and there is a patent application for its use in PET. This particular combination of phoswich may, however, have a complication since both LuAP and LuYAP emit in the excitation band of LSO, thus making the functionality more complex. In the present paper we have looked into this and suggested different ways to overcome potential drawbacks.