Three end-member clinopyroxenes from the NaM13+Si2O6 series (M1 = Al, Fe and Ga) have been examined by single-crystal X-ray diffraction at pressures up to 11 GPa. NaGaSi2O6 was also examined with Raman spectroscopy to 16.5 GPa. NaAlSi2O6 (jadeite) and NaFeSi2O6 (aegirine) are naturally occurring minerals. NaGaSi2O6 is synthetic. Various characteristics of each of the three clinopyroxenes as a function of pressure are reported, including bulk moduli (K0), unit cell volumes, atomic positions, and bond lengths.The compressibilities of a selection of clino- and orthopyroxenes from the literature were examined and considered in terms of M2-O3 bonding and unit cell volumes. As predicted by previous workers, pyroxene compressibilities generally correlate with unit cell volumes at ambient conditions. Compressibilities are also found, however, to be significantly affected by the relationship of M2-O3 bonds with the sense of rotation of silica tetrahedra upon compression. Two such relationships are observed: sympathetic, where the corner of the SiO4 tetrahedron tilts toward M2, and antipathetic, where the corner of the tetrahedron tilts away from M2. All interatomic separations in pyroxenes decrease with pressure, but sympathetic-type separations decrease more than expected based on isotropic scaling of the unit cell. Pyroxene structures may have one of several M2-O3 bond configurations: none, one, two or four bonds, and none, only sympathetic, only antipathetic, or a mixture of both types of bonds. Structures with antipathetic bonds are significantly stiffer than structures without, all else constant. The sympathetic/antipathetic bond hypothesis represents a new, previously unrecognized, first-order control on pyroxene compressibility.M1 size controls ambient unit cell volumes of clinopyroxenes. However, M1 size does not correlate well with pyroxene bulk moduli. Applying the idea of sympathetic and antipathetic M2-O3 bonding, much of the dispersion in a plot of M1 cation size versus bulk modulus can be explained. The three NaM13+Si2O6 clinopyroxenes examined in this study exhibit very similar behavior under compression. All show signs of approaching a C2/c -> C2/c phase transition at ~20 GPa. All exhibit unit strain ellipsoids with similar orientations and dimensions. All have identical bond topologies and bulk moduli that correlate with their ambient unit cell volumes.