We studied structure and function of the respiratory system in the bat Tadarida brasiliensis and compared it with those of two species of rodents, Abrothrix andinus and A. olivaceus. Tadarida brasiliensis had lower resting oxygen consumption, but higher maximum oxygen consumption and aerobic scope, than the rodents. The blood-gas barrier of the bat was thinner and its relative lung size was larger; however, alveolar surface density was similar among the three species. In consequence, T. brasiliensis has an oxygen diffusion capacity two or three times higher than that of the rodents. In Tadarida brasiliensis the characteristics of the lung were accompanied by geometrical changes in the proximal airway, such as high physical optimization as a consequence of small variations in the symmetry and the scaling ratio of the bronchial diameters. These may constitute an efficient way to save energy in respiratory mechanics and are the first report of airway adjustments to decrease entropy generation in bats.