Na época em que Sauron fez o One Ring, havia muitos outros anéis:
Now the Elves made many rings; but secretly Sauron made One Ring to rule all the others, and their power was bound up with it, to be subject wholly to it and to last only so long as it too should last. And much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency; and Sauron forged it in the Mountain of Fire in the Land of Shadow. And while he wore the One Ring he could perceive all the things that were done by means of the lesser rings, and he could see and govern the very thoughts of those that wore them.
The Silmarillion, Of the Rings of Power, p. 344
A inscrição no One Ring se aplicaria a eles. Havia também outros anéis de várias potências que não são contados entre os Anéis de Poder:
‘In Eregion long ago many Elven-rings were made, magic rings as you call them, and they were, of course, of various kinds: some more potent and some less. The lesser rings were only essays in the craft before it was full-grown, and to the Elven-smiths they were but trifles – yet still to my mind dangerous for mortals. But the Great Rings, the Rings of Power, they were perilous.’
The Lord of the Rings: The Fellowship of the Ring, The Shadow of the Past, p. 61
Todos eles, até onde eu sei, foram controlados pelo One Ring. Quanto aos Três, se Sauron nunca tocou ou mesmo os viu, não está claro como ele veio a conhecê-los:
But the Elves fled from him; and three of their rings they saved, and bore them away, and hid them. Now these were the Three that had last been made, and they possessed the greatest powers. [...] But Sauron could not discover them, for they were given into the hands of the Wise, who concealed them and never again used them openly while Sauron kept the Ruling Ring. Therefore the Three remained unsullied, for they were forged by Celebrimbor alone, and the hand of Sauron had never touched them; yet they also were subject to the One.
The Silmarillion, Of the Rings of Power, p. 345
Pode ser que ele inicialmente não estivesse ciente deles, mas apenas inferiu sua existência através das ações de Elrond, Galadriel, Círdan e depois Gandalf.