We present molecular-dynamics (MD) simulations of surface tension of aqueous ionic solutions of different concentrations for two different salts with different anion size: NaCl and NaF at 300 K in explicit water molecules. Our MD results agree quite closely with the experimental results. In particular, our MD results predict that the salt with a larger anion (NaCl) shows a smaller increase in surface tension than the salt with a smaller anion (NaF). To check the limits of applicability of the solvent primitive model (SPM), we solve exactly the system with the approximation that the solvent (water) is a background dielectric continuum using MD simulations. Compared with explicit water MD simulations, SPM gives qualitatively incorrect results for the dependence of surface tension on the type of salt. More precisely, with the solvent as a dielectric continuum, an NaCl solution shows a larger increase in surface tension than does an NaF solution. Strong water structuring around the solvated ions is the proposed explanation.