In product or process parameter design, the case of multiple performance characteristics appears more commonly than that of a single characteristic. Numerous methods have been developed to deal with such multi-characteristic parameter design (MCPD) problems. Among these, this paper considers three representative methods, which are respectively based on the desirability function (DF), grey relational analysis (GRA), and principal component analysis (PCA). These three methods are then used to solve the MCPD problems in ten case studies reported in the literature. The performance of each method is evaluated for various combinations of its algorithmic parameters and alternatives. Relative performances of the three methods are then compared in terms of the significance of a design parameter and the overall performance value corresponding to the compromise optimal design condition identified by each method. Although no method is significantly inferior to others for the data sets considered, the GRA-based and PCA-based methods perform slightly better than the DF-based method. Besides, for the PCA-based method, the compromise optimal design condition depends much on which alternative is adopted while, for the GRA-based method, it is almost independent of the algorithmic parameter, and therefore, the difficulty involved in selecting an appropriate algorithmic parameter value can be alleviated.