Positron emission tomography (PET) detectors based on monolithic scintillation crystals show excellent intrinsic spatial resolution and allow depth-of-interaction (DOI) reconstruction using a single photosensor array. The inclusion of time-of-flight (TOF) information in the image reconstruction significantly reduces the image noise variance, effectively increasing the PET system sensitivity. For optimal detection efficiency, thick crystals are needed. However, the attainable spatial resolution decreases as the crystal thickness is increased. A maximum-likelihood-estimation (MLE) algorithm was developed to determine the 3D gamma interaction position. We present results on positioning and timing performance vs. crystal thickness for three monolithic LYSO crystals (16.2 mm × 18 mm × z, z = 10 mm, 15 mm, or 20 mm) coupled to a multi-anode photomultiplier (MA-PMT). The positioning performance varied with the distance to the MA-PMT. For the 20 mm thick LYSO crystal the position resolution parallel to the MA-PMT varied between 2.5 and 4.5 mm FWHM with the distance, while the DOI could be reconstructed with a resolution varying between 2 and 5 mm FWHM. For the 20 mm thick LYSO crystal in coincidence with a fast BaF2 detector, a coincidence resolving time (CRT) of 324 ps FWHM was obtained using digital time pickoff. We observed a signal propagation time variation with gamma interaction position from 30 ps for the 10 mm thick crystal to 65 ps for the 20 mm thick crystal. We conclude that thick monolithic scintillation crystals for optimal detection efficiency show very good timing resolution, which hardly degrades when increasing the crystal thickness from 10 mm to 20 mm, and allow for accurate position reconstruction (including DOI) at minimal detector costs (using a single photosensor array to read out the crystal).