Cadmium zinc telluride (CZT) detectors are well suited for use in gamma-imaging applications thanks to their room-temperature operation, excellent energy resolution, and three-dimensional sensitivity to positions of gamma-ray interactions. In many of these applications, the position resolution with which gamma-interactions can be determined is crucial for high quality imaging. Finer pixelisation may provide improved position resolution but at the cost of increased fabrication cost and degradation of spectral performance. This work sets out to instead investigate and quantify the three-dimensional position resolution achievable using pulse shape analysis applied to digital signals, arising from interactions in a CZT detector pixelated into 2 × 2 × 5 mm3 voxels. The signal response of a 3 × 3 pixel cluster has been characterised as a function of gamma-ray interaction position using collimated 57Co and 137Cs sources. Simple pulse shape analysis algorithms using the transient image and charge collection signals have been developed and applied to achieve a sub-voxel position resolution of better than 0.65 × 0.69 × 1.26 mm3 at 122 keV and of 1.06 mm through 5 mm depth at 662 keV, not accounting for divergence of the collimated beam used to evaluate performance. Assessment of the contribution of the diverging gamma-beam placed a lower bound on the achievable positions resolution in 5 mm thickness at 122 keV of 290μm.