We present a high-pressure optical spectroscopy study on double-walled carbon nanotubes with 0.80 nm and 1.45 nm using nitrogen, argon, and alcohol-mixture as pressure transmitting medium (PTM). The pressure-induced redshift of the optical transitions in the outer tubes is very small below 10 GPa, demonstrating the enhanced mechanical stability due to the inner tube. An anomaly at the critical pressure 12 GPa signals the onset of the pressure-induced deformation of the tubular cross-sections. Using argon as PTM affects the results quantitatively: The value is lower and the absorption bands are broadened considerably. Furthermore, alcohol-mixture as PTM seems to destroy the tubes completely above 10 GPa due to its solidification. The results are compared with those for single-walled carbon nanotubes.