By performing a dual-energy scan, separate information can be obtained on the Compton and photoelectric components of attenuation for an unknown material. This procedure has been analysed for the optimum energies, and for the optimum dose distribution between the two scans. It is found that an equal dose at both energies is a good compromise, compared with optimising the dose distribution for either the Compton or photoelectric components individually. For monoenergetic beams, it is found that low energy of 40 keV produces minimum noise when using high-energy beams of 80-100 keV. This is true whether one maintains constant integral dose or constant surface dose. A low energy of 50 keV, which is more nearly attainable in practice, produces almost as good a degree of accuracy. The analysis can be extended to polyenergetic beams by the inclusion of a noise factor. The above results are qualitatively unchanged, although the noise is increased by about 20% with integral dose equivalence and 50% with surface dose equivalence. It is very important to make the spectra as narrow as possible, especially at the low energy, in order to minimise the noise.