The response to compression of the zeolite gismondine, which is the natural counterpart of the synthetic zeolite P, was explored by synchrotron X-ray powder diffraction experiments with a non-penetrating pressure-transmitting medium and by Car Parrinello molecular dynamics simulations. In the range P-amb-7.4 GPa, no pressure-induced amorphization occurs and the cell volume decrease is approximately 8%. The corresponding bulk modulus (K-0 = 63.8(2) GPa) is one of the highest found to date for zeolites studied under the same conditions. The pressure-induced cell modifications are found to be reversible upon decompression up to about 4 GPa. Gismondine is found to be more compressible along a and c with respect to b, and shows a tendency from m...