This paper reports a study, performed by in-situ synchrotron X-ray Powder Diffraction, of the high pressure behavior of the natural zeolite amicite [K4Na4(Al8Si8O32)·10H2O], the GIS-type phase with ordered (Si, Al) and (Na, K) distribution. The experiments were carried out up to 8.13(5) GPa in methanol:ethanol:water = 16:3:1 (m.e.w.) and 8.68(5) GPa in silicone oil (s.o.). The crystal structure refinements of the patterns collected in m.e.w. were performed up to 4.71(5) GPa, while for the patterns collected in s.o. only the unit cell parameters were determined as a function of pressure. The observed framework deformation mechanism—similar to that reported for the other studied phases with GIS topology—is essentially driven by the distortion of the “double crankshaft” chains and the consequent changed shape of the 8-ring channels. The pressure-induced over-hydration observed in the experiment performed in aqueous medium occurs without unit cell volume expansion, and is substantially reversible. A comparison is made with the high pressure behavior of the other GIS-type phases, and the strong influence on compressibility of the chemical composition of both framework and extraframework species is discussed.