It is well known that surfactants decrease both water/air and water/oil interfacial tensions whereas in contrast inorganic salts increase both. We study a new, third class of surface-active ionic solutes, which have been called antagonistic salts, consisting of an organic group with a small inorganic counterion. These show decreased interfacial tension at the oil/water interface due to a redistribution of the organic group in the oil but do not show any surface activity at the air/water interface and are consequently different from surfactants that lower both tensions. We use a simple modeling using PoissonBoltzmann theory that accounts for the surface activity of the antagonistic salt at the water/oil interface.