Heat exchanger networks in steam systems are traditionally designed to operate in parallel. Coetzee and Majozi (Ind. Eng. Chem. Res. 2008, 47, 4405-4413) found that by reusing steam condensate within the network the steam flow rate could be reduced. This was achieved by restructuring the networks into a series design, with the consequence of greatly increasing the pressure drop of the system. The boiler return condensate temperature was also reduced, which was found to decrease the boiler efficiency. Maintaining the boiler efficiency has been considered in the first two papers in this series, and pressure drop is introduced in this paper. The formulations from the previous two papers are used to find the minimum steam flow rate for a HEN while maintaining, the boiler efficiency. The network exhibiting the minimum pressure drop for this flow rate is then designed using the critical path algorithm. The boiler efficiency is maintained using the constraints explored in papers I Undo Eng. Chem. Res. DOI: 10.1021/ie1007008) and II (Ind. Eng. Chem. Res. DOI: 10.1021/ie1008579) of this series. The minimum pressure drop for the network exhibiting the minimum flow rate found in paper I was 344.4 kPa; however, the How rate was reduced by 29.6% as shown in paper I.