The authors have measured the reaction propagation rate (RPR) in weapons-grade, ultrafine octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) powder in a diamond anvil cell over the pressure range 0.7-35 GPa. In order to have a cross-comparison of their experiments, they carried out a series of experiments on nitromethane (NM) up to 15 GPa. The results on NM are indistinguishable from previous measurements of Rice and Folz. In comparison to high-pressure NM, the burn process for solid HMX is between 5-10 times faster at pressures above 10 GPa