We apply two different post-processing techniques to digital pulses induced by photons in NaI(Tl) detector and compare the obtained energy resolution to the standard analog approach. Our digital acquisition approach is performed using a single-stage acquisition with a fast digitizer. Both the postprocessing techniques we propose rely on signal integration. In the first, the pulse integral is calculated by directly numerically integrating the pulse digital samples, while in the second the pulse integral is estimated by a model-based fitting of the pulse. Our study used a 7.62 cm x 7.62 cm cylindrical NaI(Tl) detector that gave a 7.60% energy resolution (at 662 keV), using the standard analog acquisition approach, based on pulse shaping amplifier. The new direct numerical integration yielded a 6.52% energy resolution. The fitting approach yielded a 6.55% energy resolution, and, although computationally heavier than numerical integration, is preferable when only the early samples of the pulse are available. We also evaluated the timing performance of a fast-slow detection system, encompassing an EJ-309 and a NaI(Tl) scintillator. We use two techniques to determine the pulse start time: constant fraction discrimination (CFD) and adaptive noise threshold timing (ANT), for both the analog and digital acquisition approach. With the analog acquisition approach, we found a system time resolution of 5.8 ns and 7.3 ns, using the constant fraction discrimination and adaptive noise threshold timing, respectively. With the digital acquisition approach, a time resolution of 1.2 ns was achieved using the ANT method and 3.3 ns using CFD at 50% of the maximum, to select the pulse start time. The proposed direct digital readout and post-processing techniques can improve the application of NaI(Tl) detectors, traditionally considered 'slow', for fast counting and correlation measurements, while maintaining a good measurement of the energy resolution.2