High hydrostatic pressures were applied to single-wall carbon nanotubes by means of a diamond anvil cell (DAC), and micro-Raman spectroscopy was simultaneously used to monitor the pressure-induced shift of various nanotube bands. The data confirm recent results independently obtained from internal pressure experiments with various liquids, where the peak shifts were considered to arise from compressive forces imposed by the liquids on the nanotubes. It is also shown that the nanotube peak at 1580 cm-1 (the G band) shifts linearly with pressure up to 20 000 atm and deviates from linearity at higher pressure. This deviation is found to be coincident with a drop in Raman intensity for the disorder-induced peak at 2610 cm-1 (the overtone of the D* band), possibly corresponding to the occurrence of reversible flattening of the nanotubes. The independent results presented here confirm the potential of nanotubes as molecular sensors.