High-pressure, low-angle X-ray diffraction is used to examine the compressibility of periodic hexagonal, surfactant-templated silicas. Mesoscopic order in these materials can be retained up to 12 GPa, and pressure-induced distortions are reversible. Postsynthetic treatments can greatly enhance the mechanical properties of these nanostructured materials. Bulk moduli equal to and even higher than values measured for bulk vitreous silica are obtained if both the nanometer-scale order and local atomic-scale bonding are optimized. The results show that common architectural motifs, such as the arch or the honeycomb structure, can be used to produce rigidity and elasticity without excessive mass in materials with periodicity down to mere nanometers.