Since the resources required for the consensus reaching process are usually limited, minimum-cost consensus (MCC) based on optimization-based consensus rules is developed and widely used in various group decision-making (GDM) environments. Given the drawbacks of traditional MCC such as over-adjustment of individual opinions and reliance on a single type of consensus constraint, this chapter explores the enhanced minimum-cost consensus (EMCC) modeling. First, we propose the concept of explicit feedback path to provide a visual analytical solution for opinion adjustment in MCC. Through the path, the adjustment direction and feedback coefficient of each individual opinion are represented and quantified. According to the obtained feedback coefficients, the metrics for determining over-adjustment are designed. By incorporating explicit feedback paths into traditional MCC, several EMCC models with different types of consensus constraints are developed, all of which can effectively avoid over-adjustment. Then, the connection between the identification-direction and optimization-based consensus rules is established based on EMCC. We present the concept of coordination elasticity and discuss the performance of EMCC in terms of consensus cost and over-adjustment. The usage conditions of EMCC are analyzed. Flexible EMCC provides a negotiated solution for dealing with over-adjustment by following the principle of individual consensus cost priority. Finally, the features and advantages of the proposed EMCC models are revealed through a detailed comparative analysis with traditional MCC.