Simulation of the charge sharing properties of single-sided CZT strip detectors with small anode pads are presented. The effect of initial event size, carrier repulsion, diffusion, drift, trapping and detrapping are considered. These simulations indicate that such a detector with a 150 µm pitch will provide good charge sharing between neighboring pads. This is supported by a comparison of simulations and measurements for a similar detector with a coarser pitch of 225 µm that could not provide sufficient sharing. The performance of such a detector used as a gamma-ray imager is discussed.