Leatherback turtles (Dermochelys coriacea) are capital breeders that accumulate blubber (33 kJ g⁻¹ wet mass) by hyperphagia on a gelatinous diet at high latitudes; they breed in the tropics. A jellyfish diet is energy poor (0.1–0.2 kJ g⁻¹ wet mass) so leatherbacks must ingest large quantities. Two published estimates of feeding rate [50% body mass day⁻¹ (on Rhizostoma pulmo) and 73% body mass day⁻¹ (on Cyanea capillata)] have been criticised as too high. Jellyfish have high salt and water contents that must be removed to access organic material and energy. Most salt is removed (as NaCl) by paired lachrymal salt glands. Divalent ions are lost via the gut. In this study, the size of adult salt glands (0.622 kg for a 450 kg turtle; relatively three times the size of salt glands in cheloniid turtles) was measured for the first time by computed tomography scanning. Various published values for leatherback field metabolic rate, body fluid composition and likely blubber accumulation rates are combined with known jellyfish salt, water and organic compositions to calculate feasible salt gland secretion rates and feeding rates. The results indicate that leatherbacks can produce about 10–15 ml secretion g⁻¹ salt gland mass h⁻¹ (tear osmolality 1800 mOsm kg⁻¹). This will permit consumption of 80% body mass day⁻¹ of C. capillata. Calculations suggest that leatherbacks will find it difficult/impossible to accumulate sufficient blubber for reproduction in a single feeding season. Rapid jellyfish digestion and short gut transit times are essential.