A notable difference between the H² and H^∞ smoothing is that the achievable performance in the latter problem might “saturate” as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag. In this paper necessary and sufficient conditions under which such a saturation takes place are studied. In particular, it is shown that the H^∞ performance saturates only if the H^∞ norm of the optimal error system is achieved at the infinite frequency, i.e., if the worst case disturbance is “infinitely fast” and thus “unpredictable.”