A comprehensive assessment of pressure control in distillation columns is presented, including the consequences for composition control and energy consumption. Two types of representative control structures are modeled, analyzed, and benchmarked. A detailed simulation test, based on a real industrial distillation column, is used to assess the differences between the two control structures and to demonstrate the benefits of pressure control in the operation. In the second part of the article, a thermodynamic analysis is carried out to establish the influence of pressure on relative volatility for (pseudo)binary mixtures. A simple criterion is found, based on the difference in the scaled heats of vaporization of the light and heavy compounds: A large difference indicates that relative volatility is sensitive to pressure changes, whereas no a priori conclusion can be made for small differences. Depending on the sensitivity of relative volatility to pressure, it is shown that controlling the bottom-tray pressure instead of the top-tray pressure leads to operation at the minimum possible average column pressure, so that significant energy savings can be achieved.