A dither is a high-frequency signal introduced into a nonlinear system with the object of augmenting stability. In this paper,[1] it is shown that the effects of dither depend on its amplitude distribution function. The stability of a dithered system is related to that of an equivalent smoothed system, whose nonlinear element is the convolution of the dither distribution and the original nonlinearity. The ability of dithers to stabilize large classes of nonlinear systems is explained in terms of an effective narrowing of the nonlinear sector. A feature of the approach taken here is that a deterministic (i.e., strong) concept of stability is established under probabilistic (i.e., weak) assumptions on the dither.