Time resolution measurements were performed using four digital timing algorithms and a pair of truncated-cone shaped, 38-mm diameter LaBr(Ce) fast-timing scintillator detectors. The best resolution [FWHM=143(3) ps] was found for transitions from a 60Co source when fitting the rising part of sampled waveforms with a cubic polynomial and applying a leading-edge threshold. An average-pulse autocovariance function performed slightly worse [155(3) ps], but was found to be better than digital constant-fraction [178(4) ps] and leading-edge [177(4) ps] algorithms. Use of a 152Eu source allowed the performance of the four algorithms to be tested across a range of -ray energies with the LaBr(Ce) detectors. Here the autocovariance algorithm performed best. Changing the sampling speed showed minimal degradation in the time resolution at 20 GS/s, though at 4 GS/s the resolutions were 30–60% worse. These results show that at sampling speeds of 20 or 40 GS/s the time resolutions obtained are close to those reported for analogue pulse-processing electronics. Compared to other works, using slower sampling speeds but higher vertical resolution, slightly worse performance was obtained.