The surface tension of all aqueous alkali halide solutions is higher than that of pure water. According to the Gibbs adsorption equation, this indicates a net depletion of these ions in the interfacial region. However, simulations and experiments show that large, soft ions, such as I-, can accumulate at the liquid/vapor interface. The presence of a loose hydration shell is usually considered to be the reason for this behavior. In this work, we perform computer simulations to characterize the liquid-vapor interface of aqueous alkali chloride and sodium halide solutions systematically, considering all ions from Li+ to Cs+ and from F- to I-. Using computational methods for the removal of surface fluctuations, we analyze the structure of the interface at a dramatically enhanced resolution, showing that the positive excess originates in the very first molecular layer and that the next 3-4 layers account for the net negative excess. With the help of a fictitious system with charge-inverted ion pairs, we also show that it is not possible to rationalize the surface affinity of ions in solutions in terms of the properties of anions and cations separately. Moreover, the surface excess is generally dominated by the smaller of the two ions.