The objective of restricted selection index is to enhance genetic change in one trait while restricting to zero change in a second trait. Linear programming is another, yet conceptually different, technique to maximize one function while enforcing limits on others. The objective of this research was to compare restricted selection index and linear programming in ability to maximize performance in one trait while limiting change in a second trait to zero. Results of a numerical study demonstrate that linear programming is a more effective method to limit correlated response than restricted selection index. On average, both methods limited response in a correlated trait to zero. However, the squared deviation of actual response in the restricted trait from zero was smaller with linear programming than with restricted selection index. Response to selection in the unrestricted trait is greater with restricted selection index than with linear programming.