The influence of pressure variations upon distillation operation does not seem to be well-understood in the open literature, because contradicting statements concerning the importance of pressure control on binary distillation are found. To minimize energy consumption, it is recommended to operate columns at minimum pressure; however, even if column pressure is controlled, instability may still occur when both product purities are controlled in a decentralized control structure. In this paper, operating pressure sensitivity is classified according to the pressure sensitivity of the vapor-liquid equilibrium (VLE) relationship for the mixture being separated. Operating pressure sensitivity is shown to become significant at high internal flow rates. It is furthermore shown that this sensitivity may lead to a situation where different values of the internal flow rate may produce the same product purity, which commonly is labeled "input multiplicity" of the separation. This input multiplicity is shown to occur through a theoretical analysis combined with simulation of the case study and an extended series of experiments. The input multiplicity can be explained by two opposing effects from varying internal flows: the first comes from the well-understood effect of changing the slope of the operating lines, whereas the second is due to the effect of pressure on the VLE relationship. Understanding the input multiplicity or, rather, the pressure sensitivity is relevant for efficient exploitation of the separation capacity of the column through proper control structure selection, i.e., for determination of where to place sensors in a distillation column for controlling pressure. It is shown that the distillation column is most efficiently utilized by controlling the pressure at the column bottom/top for a negative/positive-pressure-sensitive mixture. It is furthermore concluded that controlling the column pressure at the proper end of the column may be crucial to column stability when both product purities are controlled in a decentralized control structure. In an experimental verification, it is demonstrated that, for separating a mildly negative-pressure-sensitive mixture, the distillation column separation capacity is most efficiently exploited when controlling the column pressure at the bottom of the distillation column. For the investigated mixture, it is shown that a 20% higher capacity may be obtained at a lower energy requirement. Thus, a significantly (20%) lower energy expenditure per produced unit is realized through the improved control structure, when compared to conventional control of the column pressure at the top of the distillation column.