Powder diffraction has experienced a revival of interest in recent years and attracts increasing attention. The present X-ray powder diffraction study includes investigations into techniques for improving resolution, accuracy and reliability of data collection for powder indexing and structural work. Powder data were collected using both a Guinier-Hagg camera and a Stoe focussing powder diffractometer (STADI P). All test materials studied were organic, and were single phases rather than mixtures. The diffractometer data were found to be more accurate than the Guinier-Hagg camera data. In general the STADI P results from low-symmetry materials showed capillary samples to give better angular resolution and positional accuracy than flat samples. With triclinic hexamethylbenzene there are also indications that resolution tends to improve as the size of the crystallites becomes smaller. The reported low-temperature phase transition of hexamethylbenzene at around 115. 5 K, interpretations of which have differed for over 50 years, has been re-investigated using high-resolution X-ray powder diffraction. The crystal structures have been determined at 120 K and 80 K (i. e. just above and below the transition), with the aid of Rietveld method refinements from STADI P profile data. The low-temperature phase III structure was previously unknown and no X-ray crystal structure work had been reported at these temperatures. The 120 K structure is that of the triclinic phase II, the phase stable at room temperature. The 80 K structure was confirmed to be trigonal (described here on hexagonal axes). Both low-temperature structures are reported, with hydrogen atoms included in the refinement. A mechanism has been proposed for the phase II-III transition.