Cost-effective retrofit of heat exchanger networks (HENs) remains a significant challenge. This paper explores different methods for achieving cost-effective retrofit. The first part of this article presents a novel methodology for the application of heat transfer enhancement in HEN retrofit with a fixed network structure considering pressure drop constraints. Heat transfer enhancement is a low-cost option. However, heat transfer enhancement on its own without changes to the network structure provides a limited scope for energy reduction. The second part of this paper presents a new pinch retrofit method that identifies network structural changes sequentially to meet the retrofit target. However, the high capital cost associated with installing new heat exchangers, relocating existing exchangers, and augmenting the heat transfer area of existing heat exchangers most often leads to uneconomic retrofits. Low-cost retrofit requires few modifications. Therefore, the third part of this paper combines the new pinch retrofit method with the use of heat transfer enhancement to provide low-cost retrofit by combining the merits of both approaches. A case study highlights the benefits of the new approach.