This paper examines the design of mixed thermally coupled-heat-integrated distillation sequences. The approach considers a variety of methodologies, from conventional columns (each distillation column with a condenser and a reboiler) to fully thermally coupled systems (only one reboiler and one condenser in the entire system). A discussion about superstructure generation and the convenience of using a representation based on separation tasks instead of equipment is presented, as well as a set of logical rules in terms of boolean variables that allow all of the feasible structures to be generated systematically. Based on the logical rules, an algorithm is developed for generating valid sequences (even by hand) without explicitly solving the logical equations. All the specific aspects were related to intercolumn heat integration when partially thermally coupled systems are considered. A disjunctive programming formulation for extracting the optimal solution is presented. The model is based on the Fenske-Underwood-Gilliland equations. However, the disjunctive formulation easily allows the use of any other shortcut, aggregated, or even rigorous model without almost modifying the structure of the formulation. Finally, three examples are presented.