Three-dimensional position-sensitive CdZnTe (CZT) gamma-ray spectrometers employing new VAS3.1/TAT3 ASIC readouts were developed and tested. Each spectrometer is a 1.5times1.5times1 cm3 CdZnTe crystal with 11 by 11 pixelIated anodes wire-bonded to the readout electronics using an intermediate ceramic substrate with plate-through-via. The signals from the anode pixels and the cathode were all read out through these ASICs. The pixel position provides the lateral coordinates of the interaction, while the cathode to anode signal ratio and the electron drift time are used to obtain the interaction depth. Using the 3-D position information, the variation in weighting potential, electron trapping and material non-uniformity can be accounted for to the scale of the position resolution, ~1.27 mmtimes1.27 mmtimes0.2 mm. The new VAS3.1/TAT3 ASIC has less gain and baseline drift, lower cross-talk noise, more uniform thresholds, better linearity and better timing resolution than our previous VAS2/TAT2 system. For example, the 32 keV K X-ray from a 137Cs source was observed for the first time. Two 3-D CZT spectrometers were tested and both achieved better than 1% FWHM energy resolution (at 662 keV, room temperature operation, with an uncollimated source) for single-pixel events. The experimental results for these two 3-D CZT spectrometer systems are presented and discussed