A PET detector with good timing resolution and two-level depth-of-interaction (DOI) discrimination can be constructed using a single-ended readout of scintillator stacks of Lanthanum Bromide (LaBr3), with various Cerium dopant concentrations, including pure Cerium Bromide (CeBr3). The stacked crystal geometry creates a unique signal shape for interactions occurring in each layer, which can be used to identify the DOI, while retaining the inherently good timing properties of LaBr3 and CeBr3. In this work, single pixel elements are used to optimize the choice of scintillator, coupling of layers, and type of photodetector, evaluating the performance using a fast, single-channel photomultiplier tube (PMT) and a single 4×4 mm2 silicon photomultiplier (SiPM). We also introduce a method to quantify and evaluate the DOI discrimination accuracy. From signal shape measurements using fast waveform sampling, we found that in addition to differences in signal rise times, between crystal layers, there were also differences in the signal fall times. A DOI accuracy of 98% was achieved using our classification method for a stacked crystal pair, consisting of a 15-mm long LaBr3(Ce:20%) crystal on top of a 15-mm long CeBr3 crystal, readout using a PMT. A DOI accuracy of 95% was measured with a stack of two, identical, 12-mm long, CeBr3 crystals. The DOI accuracy of this crystal pair was reduced to 91% when using a SiPM for readout. For the stack of two, 12-mm long, CeBr3 crystals, a coincidence timing resolution (average of timing results from the top and bottom layer) of 199 ps was measured using a PMT, and this was improved to 153 ps when using a SiPM. These results show that with stacked LaBr3/CeBr3 scintillators and fast waveform sampling nearly perfect DOI accuracy can be achieved with excellent timing resolution—timing resolution that is only minimally degraded compared to results from a single CeBr3 crystal of comparable length to the stacked crystals. The interface in the stacked crystal geometry itself plays a major role in creating the differences in signal shape and this can be used to construct stacked DOI detectors using the same scintillator type, thereby simplifying and broadening the application of this technique.