When dose-response functions have a downturn, one interesting feature to study is the significance of the downturn. The interesting feature can be studied using model discrimination between two rival models (model describing dose-response functions with a downturn versus model describing only increasing part of the response functions). In this article, we study T-optimal designs that can best discriminate between these two rival models. Three different sets of model parameter values are considered to demonstrate various shapes of dose-response functions. Under the different sets of the parameter values, the T-optimal designs are obtained, and their performances are compared to two other known designs for the model discrimination (Ds-optimal design and Uniform design) through Monte Carlo Simulation.