OBJECTIVE: Coincidence time resolution (CTR) in time-of-flight positron emission tomography (TOF-PET) has significantly improved with advancements in scintillators, photodetectors, and readout electronics. Achieving a CTR of 100 ps remains challenging due to the need for sufficiently thick scintillators-typically 20 mm-to ensure adequate sensitivity because the photon transit time spread within these thick scintillators impedes achieving 100 ps CTR. Therefore thinner scintillators are preferable for CTR better than 100 ps. To address the trade-off between TOF capability and sensitivity, we propose a readout scheme of PET detectors. APPROACH: The proposed scheme utilizes two orthogonally stacked one-dimensional PET detectors, enabling the thickness of the scintillators to be reduced to approximately 13 mm without compromising sensitivity. This is achieved by stacking the detectors along the depth-of-interaction (DOI) axis of a PET scanner. We refer to this design as the cross-stacked detector, or xDetector. Furthermore, the xDetector inherently provides DOI information using the same readout scheme. MAIN RESULTS: Experimental evaluations demonstrated that the xDetector achieved the best CTR of 175 ps full width at half maximum (FWHM) and an energy resolution of 11% FWHM at 511 keV with 3 × 3 × 12.8 mm3 lutetium oxyorthosilicate crystals, each coupled one-to-one with silicon photomultipliers. The CTRs are between the xDetector and reference detector with a single timing resolution of 111.2 ± 0.8 ps FWHM. In terms of xy-spatial resolution, the xDetector exhibited an asymmetric resolution due to its readout scheme: one resolution was defined by the 3.2 mm readout pitch, while the other was calculated using the center-of-gravity method. SIGNIFICANCE: The xDetector effectively resolves the trade-off between TOF capability and sensitivity while offering scalability and DOI capability. By integrating state-of-the-art scintillators, photodetectors, and readout electronics with the xDetector scheme, achieving a CTR of 100 ps FWHM alongside high DOI resolution becomes a practical possibility.