The Czochralski pulling process is the most valuable and cost efficient method for producing large oriented single crystals of the group IV and III-V semiconductors. However, there have been only a small number of reported attempts to use the Czochralski process for growing the wide bandgap compound semiconductors, needed for the room temperature operated gamma-ray detectors. The main difficulty is in the low chemical stability and high vapor pressure of the group II, V and VI elements, leading to off-stoichiometric composition, and various related defects. Among the heavy metal halides, indium iodide and indium bromide present an interesting exception. InI has a high molecular disassociation energy and a low vapor pressure, allowing for Czochralski pulling. We will describe the procedures used and the results obtained by Czochralski growth and characterization of indium iodide and the related ternary compounds that appear to be quite encouraging.