The spatial resolution in positron emission tomography (PET) can be improved by the addition of depth-of-interaction (DOI) information. This can be achieved by using the phoswich approach in which depth identification relies on differences in scintillation decay time and pulse shape discrimination techniques. In this paper we have looked at a special phoswich combination LuAP/LSO or LuYAP/LSO. This combination of scintillators is especially interesting since LuAP and LuYAP have emission in the excitation band of LSO, which may have an impact on the timing resolution of the detector. As will be shown in this paper, the phoswich concept based on these two scintillators can be utilized, however, with some limitations. This paper is an extension of our previous phoswich investigation .