It was shown by Zames and Shneydor and later by Mossaheb that a high-frequency dither signal of a quite arbitrary shape call be used to narrow the effective nonlinear sector of Lipschitz continuous feedback systems. In this paper, it is shown that also discontinuous nonlinearities of feedback systems can be narrowed using dither, as long as the amplitude distribution function of the dither is absolutely continuous and has bounded derivative. The averaged system is proven to approximate the dithered system with an error of the order of dither period. (c) 2006 Elsevier Ltd. All rights reserved.