The availability of large, single crystals of cadmium zinc telluride (CZT) with uniform properties is key to improving the performance of gamma radiation detectors fabricated from them. Towards this goal, we discuss results obtained by computational models that provide a deeper understanding of crystal growth processes and how the growth of CZT can be improved. In particular, we discuss methods that may be implemented to lessen the deleterious interactions between the ampoule wall and the growing crystal via engineering a convex solidification interface. For vertical Bridgman growth, a novel, bell-curve furnace temperature profile is predicted to achieve macroscopically convex solid-liquid interface shapes during melt growth of CZT in a multiple-zone furnace. This approach represents a significant advance over traditional gradient-freeze profiles, which always yield concave interface shapes, and static heat transfer designs, such as pedestal design, that achieve convex interfaces over only a small portion of the growth run. Importantly, this strategy may be applied to any Bridgman configuration that utilizes multiple, controllable heating zones. Realizing a convex solidification interface via this adaptive bell-curve furnace profile is postulated to result in better crystallinity and higher yields than conventional CZT growth techniques.