The increase in oil recovery from low salinity water injection has been often attributed to the alteration of wettability to water wetting. The increase in elasticity of the interface may also contribute to increase in oil recovery as has been suggested in the literature.In this work, we investigate oil recovery using two carbonate cores, one with large vugs, and the other without. The pore size and pore size distributions are very different in the two carbonate cores. The investigation centers on oil recovery from low and high salinity water injection, and by addition of an effective demulsifier molecule at 100 ppm in the injected high salinity water. The effective demulsifier molecule gives substantially higher oil recovery than low salinity and high salinity water injection. The oil-water interface elasticity increases significantly from the addition of 100 ppm demulsifier molecule to the aqueous phase. Salinity of the injected water is found to have a weak effect on oil recovery. We attribute high recovery performance of the 100 ppm surfactant to the increase in interface elasticity. The high recovery performance is observed in the carbonate reservoir rocks, both with and without vugs. The demulsifier molecule which is non-ionic has a very low adsorption in the carbonate rocks, around 2 mg/g at 100 ppm in high salinity injection water.This work introduces a new process for improved oil recovery by the introduction of a demulsifier molecule at ultra-low cocentration. The molecule has limited effect on water-wetting. The critical micelle concentration (CMC) of the non-ionic surfactant in the injected brine is at 30 ppm. The low adsorption, and the CMC indicate that the molecule adsorbs at the oil-water interface. The conventional chemical flooding which may require one or two orders of magnitude more material is through significant reduction of interfacial tension. The interface elasticity is singled out to be the main contribution to improved oil recovery in this work.