An optimisation-based decision support methodology is presented for the synthesis of energy supply systems on the conceptual level. Previous work in this field has tended to focus on the generation of the single optimal solution. However, given that mathematical models never perfectly represent the real world and that planners are often not aware of all practical constraints, the mathematically optimal solution usually only approximates the real-world optimum, and thus has only limited significance. The presented approach therefore exploits the near-optimal solution space for more rational synthesis decisions. For this purpose, integer-cut constraints are employed to systematically generate a set of near-optimal solutions alongside the optimal solution. In place of the traditional analysis of the single optimal solution, we analyse the generated solution set to identify common features (the "must-haves") and differences (the "real choices") among the good solutions, and features not observed in any of the generated solutions (the "must-avoids"). This approach provides valuable insights into the synthesis problem and opens up a wide range of rational decision options. The proposed concept is applied to three different real-world problems at the industrial, district, and urban scale. For all three test cases, many near-optimal solutions are identified with different equipment configurations but similar objective function values. Thus, a ranking of the identified solutions strictly based on a single objective value is not productive. Instead, we show that the near-optimal solutions analysis supports the decision process to identify a wider basis of system options, which may be consulted upon to reach rational synthesis decisions. (C) 2015 Elsevier Ltd. All rights reserved.