|Abstract:||It is often suggested that if all sound change were due to optimizations of functional principles (minimization of articulatory effort, minimization of perceptual confusion), then sound systems should have increasingly improved during the course of history, probably to the point that they should by now have reached a stable optimum. Since the facts show, however, that sound systems tend never to stop changing, the conclusion must be, so the story goes, that optimization cannot be a major internal factor in sound change. But it may all depend on how we define optimization. In Boersma (1989), I showed that there is a simple optimization strategy that may be cyclic, and that this cyclicity is attested in the Germanic consonant shifts. In Boersma (1997), I showed that this optimization strategy is equivalent to a non-teleological random ranking of constraints in an Optimality-Theoretic grammar. In this paper, I show that the cyclicity attested in the Germanic consonant shifts is not due to a large coincidence, but that, given random ranking of invisible constraints in OT, this cyclicity is expected in a large fraction of all sound changes.