The theory of d.c. low-pressure metal-vapour rare-gas discharges is developed, for the cases of simple one-stage and simple two-stage ionization, in a manner which enables the performance of a discharge in a tube of any given cross-sectional shape to be derived from that of an "equivalent" discharge in an "equivalent" tube of circular cross-section. The latter can be obtained from a more detailed investigation of the discharge in a circular tube.It is shown that the discharges are capable of producing substantially more resonance radiation per unit length at a given efficiency in tubes of a "flattened" cross-sectional shape, than in tubes of a circular cross-sectional shape, particularly when there is a narrow, or waisted, middle section. Multi-stage ionization ultimately restricts the extent to which this improvement can be carried to aspect ratios of about 3: 1.