We propose to develop and optimize 0.5 cm thick Cadmium Zinc Telluride (CZT) detectors with very small pixel pitches, i.e. 350 micron and 600 micron. The proposed innovative R&D program is highly relevant for the EXIST (Energetic X-ray Imaging Survey Telescope) mission, the leading candidate for NASA's black hole finder probe. The new EXIST reference design from the recent Advanced Mission Concept Study uses CZT detectors with a pixel pitch of 600 micron. The proposed work focuses on the optimization of the design of the pixel patterns (pad and gap widths), steering grids, guard rings, and bias rings. For the different designs, the detection efficiencies, energy resolutions, charge sharing properties, and minimum achievable energy thresholds will be evaluated. Dedicated measurements with collimated X-ray beams will be performed to evaluate the accuracy with which the depth of the interaction can be reconstructed based on different methods. Measurements with polarized X-ray beams will be used to put estimates of the X-ray polarization sensitivity of EXIST on a solid footing. Last but not least, the experimental results will be used to fine-tune a 3-D model of the detector response. The proposed R&D is exciting and new in that very thick detectors with very small pixel pitches will be studied for the first time in detail. Effects like charge carrier diffusion and charge carrier repulsion are relatively more important for such detectors than for thinner detectors and/or detectors with larger pixel pitches.