The structure and dimensions are given for the rete mirabile. It is interpreted as a counter current diffusion exchange mechanism between the afferent and efferent rete. This diffusion exchange was quantitatively evaluated for O2, CO2, and N2. The arrangement makes possible the maintenance of a steep tension gradient within the rete, so that the 02 loss from the leaving blood can be extremely low. Quantitative evaluation of the efficiency of the rete diffusion makes it clear that the limiting equilibrium pressure in the swimbladder could be extremely high, and that the limiting factor lies mainly in the dissociation pressure of the chemical or physical reaction which ultimately splits off the O2. The nature of the responsible compound and reaction is unknown. Anatomical arrangement of the glandular structure and the rete is suggestive of a cellular secretion of O2 rather than of a mechanism that splits off 02 in the blood. Data on the deposition of N2 against high pressures which were previously found in deep sea fish were confirmed and extended. The argon-to-N2 ratio in the swim-bladder gas suggests that the N2 has entered the swimbladder via some physical mechanism. The possibility that this is brought about by a lowering of the N2 solubility coefficient in the efferent rete is discussed.