We studied the compressibility of silver (10 nm) and gold (30 nm) nanoparticles, n-Ag and n-Au, suspended in a methanol-ethanol mixture by x-ray diffraction (XRD) with synchrotron radiation at pressures up to 30 GPa. Unexpectedly for that size, the nanoparticles show a significantly higher stiffness than the corresponding bulk materials. The bulk modulus of n-Au, K(0)=290(8) GPa, shows an increase of ca. 60% and is in the order of W or Ir. The structural characterization of both kinds of nanoparticles by XRD and high-resolution electron microscopy identified polysynthetic domain twinning and lamellar defects as the main origin for the strong decrease in compressibility.