We report here combined quasi-hydrostatic high-pressure small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) studies on faceted 3D supercrystals (SCs) self-assembled from colloidal 7.0 nm spherical PbS nanocrystals (NCs). Diamond anvil cell (DAC) SAXS experiments in the pressure range from ambient to 12.5 GPa revealed nearly perfect structural stability of the SCs, with face-centered cubic organization of the NCs. Pressure-induced ordering (annealing effect) of the superstructure was observed. The ambient pressure bulk modulus of the SCs was calculated to be ∼5 GPa for compression and ∼14.5 GPa for decompression from fitting of Vinet and Birch-Murnaghan equations of state. XRD measurements revealed strong preferential crystallographic orientation of the NCs through all phase transformations to as high as 55 GPa without any indication of NC sintering. The first phase transition pressure of the NCs was found between 8.1 and 9.2 GPa and proceeds through homogeneous nucleation. Bulk modulus of PbS NCs was calculated to be ∼51 GPa based on fitting to the equations of state (K(PbS,bulk) ∼ 51-57 GPa). Closest surface-to-surface distance between the NCs in the SCs was calculated based on combined XRD and SAXS data, to reversibly tune from ∼1.56 nm to ∼0.9-0.92 nm and back to ∼1.36 nm in the ambient-12.5 GPa-ambient pressure cycle. The bulk modulus of the ligand matrix was extrapolated to be ∼2.2-2.95 GPa. These results show a general method of tuning NC interactions in packed nanoparticle solids.