Freezing and melting of aqueous solutions of alkali halides confined in the cylindrical nanopores of MCM-41 and SBA-15 silica was probed by differential scanning calorimetry (DSC). We find that the confinement-induced shift of the eutectic temperature in the pores can be significantly greater than the shift of the melting temperature of pure water. Greatest shifts of the eutectic temperature are found for salts that crystallize as oligohydrates at the eutectic point. This behavior is explained by the larger fraction of pore volume occupied by salt hydrates as compared to anhydrous salts, on the assumption that precipitated salt constitutes an additional confinement for ice/water in the pores. A model based on this secondary confinement effect gives a good representation of the experimental data. Salt-specific secondary confinement may play a role in a variety of fields, from salt-impregnated advanced adsorbents and catalysts to the thermal weathering of building materials.