X-ray diffraction studies have been carried out on alkali halide samples 10 micrometers in diameter (volume 10-9 cubic centimeter) subjected to megabar pressures in the diamond anvil cell. Energy-dispersive techniques and a synchrotron source were used. These measurements can be used to detect crystallographic phase transitions. Cesium iodide was subjected to pressures of 95 gigapascals (fractional volume of 46 percent) and rubidium iodide to pressures of 89 gigapascals (fractional volume of 39 percent). Cesium iodide showed a transformation from the cubic B2 phase (cesium chloride structure) to a tetragonal phase and then to an orthorhombic phase, which was stable to 95 gigapascals. Rubidium iodide showed only a transition from the low-pressure cubic B1 phase (sodium chloride structure) to the B2 phase, which was stable up to 89 gigapascals.