Experimentation plays a fundamental role in scientific discovery. Scientists experiment to gather data, investigate phenomena, measure quantities, and test theories. In this article, we address the problem of designing experiments to discriminate between two completing theories. Given an initial situation for which the two theories make the same prediction, the experiment design problem is to determine how to modify the situation such that the two theories make different predictions for the modified situation. The modified situation is called a discrimination experiment. We present a knowledge-intensive method called DEED for designing discrimination experiments. The method analyzes the differences in the two theories' explanations of the prediction for the initial situation. Based on this analysis, it determines modifications to the initial situation that will result in a discrimination experiment. We illustrate the method with the design of experiments to discriminate between several pairs of qualitative theories in the fluids domain.