The high-pressure behavior of 3,3 '-biisoxazole-5,5 '-bis-(methylene) dinitrate (BIDN) and 3,3 '-biisoxazole-4,4 ',5,5 '-tetrakis-(methylene nitrate) (BITN) have been studied at room temperature to 25 GPa by Raman spectroscopy and powder X-ray diffraction. The Raman spectra, powder patterns, and calculated unit-cell volumes at select pressures show qualitative agreement with first-principles density function theory calculations. Over this pressure range, no evidence of polymorphism was observed. The lack of observed phase changes can be partially attributed to the strengthening of hydrogen bonding observed with pressure increase. These insights point to the potential importance of hydrogen bonding in potential melt-castable materials.