A formal method is described for the synthesis of multicomponent distillation systems when energy integration is considered between streams both within the separation sequence and in other parts of the process. The pressure in each column is considered as an optimization variable for both the energy integration and column sizing computations. Four rules are used to enumerate all feasible energy matches between the streams associated with the distillation columns. A bounding strategy which uses both upper and lower bounds is combined with dynamic programming to synthesize the optimal distillation sequence with energy integration. A five-component separation problem demonstrates the effectiveness of the methods.