Previous diffraction studies of the complex high-pressure structures Bi-III and Sb-II are reviewed. Our structural studies on Bi under high pressure using angle-dispersive x-ray diffraction techniques with monochromatic synchrotron radiation and an image plate detector are described in detail. We report a solution for the Bi-III structure that is similar to the incommensurate Ba-IV-type structure. It is composed of two interpenetrating cells - a tetragonal host, and a tetragonal guest which is incommensurate with the host along the tetragonal axis. Some crystallographic aspects of the structure are discussed.