This chapter devotes to the problem of constructing T-optimal discriminating designs for Fourier regression models which differ by at most three trigonometric functions. Here we develop the results obtained in a paper (Dette, Melas and Shpilev (2015). T-optimal discriminating designs for Fourier regression models. 1–17) [11] and give a few its generalizations. We consider in detail the case of discriminating between two models where the order of the larger one equals two. For this case, we provide explicit solutions and investigate the dependence of the locally T-optimal discriminating designs on the parameters of the larger model. The results obtained in the chapter can also be applied in classical approximation theory.