The "Petlyuk" or "dividing-wall" or "fully thermally coupled" distillation column is an interesting alternative to the conventional cascaded binary columns for separation of multi-component mixtures. The industrial use has been very limited, and difficulties in control has been reported as one reason. Since we have more manipulated variables than controlled variables, the column is a candidate for on-line optimization. We show that the steady-state optimal solution surface is quite narrow, and depend strongly on disturbances and design parameters. Thus it seems difficult to achieve the potential energy savings compared to traditional approaches without a good control strategy.