High-brightness synchrotron X-rays together with precision achromatic focusing optics on beamline 7.3.3 at the Advanced Light Source have been applied for Laue microdiffraction analysis of mineralogical phases in Egyptian pigments. Although this task is usually performed using monochromatic X-ray diffraction, the Laue technique was both faster and more reliable for the present sample. In this approach, white-beam diffraction patterns are collected as the sample is raster scanned across the incident beam (0.8 mu m x 0.8 mu m). The complex Laue diffraction patterns arising from illumination of multiple grains are indexed using the white-beam crystallographic software package XMAS, enabling a mineralogical map as a function of sample position. This methodology has been applied to determine the mineralogy of colour pigments taken from the ancient Egyptian coffin of Tjeseb, a priestess of the Apis bull dating from the Third Intermediate to Late period, 25th Dynasty to early 26th Dynasty ( 747 to 600 BC). For all pigments, a ground layer of calcite and quartz was identified. For the blue pigment, cuprorivaite (CuCaSi4O10) was found to be the primary colouring agent with a grain size ranging from similar to 10 to 50 mu m. In the green and yellow samples, malachite [Cu-2( OH)(2)CO3] and goethite [FeO(OH)] were identified, respectively. Grain sizes from these pigments were significantly smaller. It was possible to index some malachite grains up to similar to 20 mu m in size, while the majority of goethite grains displayed a nanocrystalline particle size. The inability to obtain a complete mineralogical map for goethite highlights the fact that the incident probe size is considerably larger than the grain size. This limit will continue to improve as the present trend is toward focusing optics approaching the diffraction limit ( similar to 1000 x smaller beam area).