Economic and environmental benefits result from increasing the energy efficiency of industrial systems. This article presents the application of bridge analysis concepts to improve the methodology of network pinch for heat exchanger network retrofit. In two simple examples, we compare bridge analysis with the network pinch approach, in terms of saving energy by heat exchanger network improvement. The first example is solved with both methods, while the second can only be solved by bridge analysis. In the first example, three different solutions are proposed, and the third solution leads to 3800 kW energy savings, i.e., the full savings capacity. In the second example, no heat can be saved using the network pinch approach, but two solutions are proposed using bridge analysis, which lead to 395 kW energy savings, i.e., the full savings capacity. Then, we discuss the advantages and limits of pinch analysis and the network pinch approach. Bridge analysis provides a broader perspective on pinch analysis, explains the natural presence of a pinch in a network, shows that removing cross pinch transfers is not necessary to save energy, and helps improve heuristics for creating new cooler-heater paths in the network pinch procedure.