We test local and semilocal approximations of the exchange potential for a variety of systems including atoms, molecules, and atomic chains. In particular, we focus on a recent universal extension of the Becke−Johnson exchange potential [Räsänen, E.; Pittalis, S.; Proetto, C. R. J. Chem. Phys. 2010, 132, 044112]. It is shown that when this potential is used together with the Becke−Roussel approximation to the Slater potential [Becke, A. D.; Roussel, M. R. Phys. Rev. A 1989, 39, 3761−3767], a good overall agreement is obtained with experimental and numerically exact results for several systems, and with a moderate computational cost. Thus, this approximation is a very promising candidate in the quest for a simple and all-around semilocal potential.