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Two-dimensional electron systems with fascinating properties exist in multilayers of standard semiconductors, on helium surfaces, and in oxides. Compared to the two-dimensional (2D) electron gases of semiconductors, the 2D electron systems in oxides are typically more strongly correlated and more sensitive to the microscopic structure of the hosting lattice. This sensitivity suggests that the oxide 2D systems are highly tunable by hydrostatic pressure. Here we explore the effects of hydrostatic pressure on the well-characterized 2D electron system formed at LaAlO3-SrTiO3 interfaces [A. Ohtomo and H. Y. Hwang, Nature (London) 427, 423 (2004)] and measure a pronounced, unexpected response. Pressure of ~2 GPa reversibly doubles the 2D carrier density ns at 4 K. Along with the increase of ns, the conductivity and mobility are reduced under pressure. First-principles pressure simulations reveal the same behavior of the carrier density and suggest a possible mechanism of the mobility reduction, based on the dielectric properties of both materials and their variation under external pressure. [ABSTRACT FROM AUTHOR]