This investigation reports on a thermodynamic phenomenon that can be observed in aqueous solutions of hydrophilic organic solvents: A completely miscible binary liquid mixture of water and an organic solvent, e.g., 1-propanol, can reveal a liquid-phase split, when it is pressurized with a "near-critical" gas, i.e., a gas near its critical temperature. This phase split phenomenon is briefly explained and new experimental data are presented for the partitioning of some natural products (ethyl acetate, D-fructose, D-glucose, and maltol) on, at near-critical pressures, coexisting liquid phases of a three-phase vapor-liquid-liquid equilibrium in the ternary system carbon dioxide + water + 1-propanol. In addition to the experimental data, a semiempirical approach for the correlation of the partition coefficients is shortly outlined. As the partition coefficients significantly deviate from unity, this phase equilibrium phenomenon can be applied for a new mild high-pressure liquid-liquid extraction process for natural products.