A selective, multiple-criteria method is proposed for handling constraint violations in well-defined design problems. First, the types of design problems upon which the method may apply are presented and a graph topology is adopted for representing the problem decomposition in the level of design parameter interrelations (design parameter graphs). Next, the problem of constraint violations for the design parameters is discussed. It is shown that these violations can be resolved by modifying the values of the primary design parameters and recalculating the values of the violated parameters. Any “blind” attempt of modifying the values of the primary design parameters for resolving occurring violations may, eventually, create additional violations. The proposed method guides the designer toward those primary design parameters that present the least possibility of creating more violations when their values are modified. This is achieved by applying multiple criteria and by producing a final, sorted list of primary design parameters. The designer may then choose the first element of this list to handle efficiently the violations of the design parameters. Two examples are given on a design space where constraint violations occur. Through these examples, the capability of the proposed method in helping the designer to handle constraint violation is shown. The concluding remarks, except for summarizing the potential of the method, determine its boundaries and include a reference on relative work currently under investigation.