A multi-effect distillation where the condenser of a high pressure column is integrated with the reboiler of a low pressure column has been studied. The method of self-optimizing control has been used to provide a systematic procedure for the selection of controlled variables, based on steady-state economics. The system has 10 degrees of freedom at steady state. The heat integrated distillation system was optimized to find the nominal operating point. It was found that the constraints on the product composition, area in the combined reboiler/condenser, the purity constraint in the low pressure column and the pressure in the low pressure column are active constraints. For the remaining unconstrained variable it was found that a temperature in the low-pressure column has good self-optimizing properties. The study also shows how there can be multiplicities in the objective function for certain variables in the system.