Industries are starting to replace shell-and-tube heat exchangers with compact heat exchangers in several applications. Benefits have been reported when using compact heat exchangers at the equipment level. However, greater economic benefits can be realized when applying compact heat exchangers in the context of the overall heat transfer system. This is not an easy task for both industries and designers who are new to compact heat exchangers. This is because the data for heat transfer conditions for each stream are not available in the early design stage to guide the overall network design. Hence, a method which can determine the optimal heat transfer conditions for each stream and the network configuration simultaneously is essential in promoting the use of compact heat exchangers. Here a novel method is developed which can achieve this objective. The new method utilizes the advantages of two new physical insights into heat transfer surface selection, i.e., the identical-fin concept and the Z-Y graph. The concept of using the same fins for all streams in the early design stage is reasoned anti justified physically in this article. The Z-Y graph is then developed to represent four important design parameters, namely, fin types, volume, pressure drop, and frontal area. Using these two concepts, a level-by-level methodology is developed to provide a transparent design procedure so that the designer is able to monitor and control the design process. Each design level is solved using mathematical programming to address the complex interactions and trade-offs. In this way, the advantages of heat transfer surfaces (fins) can be fully explored at the very beginning of design stage and optimization of fin selection is considered in the context of the overall design problem. Consequently, the heat exchanger networks designed using compact heat exchangers can be compared clearly and fairly with their shell-and-tube counterparts. Thus designers can have more confidence using compact heat exchangers in the overall network. The design method starts with very little information that is already known to the system (for example, temperatures and physical properties) and systematically guides the designer towards the final design.