Apolar lipids within the membranes of archaea are thought to play a role in membrane regulation. In this work we explore the effect of the apolar lipid squalane on the dynamics of a model archaeal-like membrane, under pressure, using neutron spin echo spectroscopy. To the best of our knowledge, this is the first report on membrane dynamics at high pressure using NSE spectroscopy. Increasing pressure leads to an increase in membrane rigidity, in agreement with other techniques. The presence of squalane in the membrane results in a stiffer membrane supporting its role as a membrane regulator.