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It is a central paradigm of comparative physiology that the effect of humidity on evaporative water loss (EWL) is determined for most mammals and birds, in and below thermoneutrality, essentially by physics and is not under physiological regulation. Fick's law predicts that EWL should be inversely proportional to ambient relative humidity (RH) and linearly proportional to the water vapour pressure deficit (Δwvp) between animal and air. However, we show here for a small dasyurid marsupial, the little kaluta (Dasykaluta rosamondae), that EWL is essentially independent of RH (and Δwvp) at low RH (as are metabolic rate and thermal conductance). These results suggest regulation of a constant EWL independent of RH, a hitherto unappreciated capacity of endothermic vertebrates. Independence of EWL from RH conserves water and heat at low RH, and avoids physiological adjustments to changes in evaporative heat loss such as thermoregulation. Re-evaluation of previously published data for mammals and birds suggests that a lesser dependence of EWL on RH is observed more commonly than previously thought, suggesting that physiological independence of EWL of RH is not just an unusual capacity of a few species, such as the little kaluta, but a more general capability of many mammals and birds.