Can an omnipotent being create a stone too heavy for him to lift? If not, he is not omnipotent. But if so, he is not omnipotent either, since there is something he cannot lift. Hence there can be no omnipotent being. J.L. Cowan's recent reformulation of this paradox of omnipotence has been sharpened through a number of objections and clarifications, and, in its final form, constitutes a significant problem for the analysis of the concept of an omnipotent agent. I will (...) develop fragments of two systems in which the problem can be defined more exactly, and try to indicate some formal guidelines within which constructive steps towards a solution may be possible. I will argue that the paradox shows the need for a special kind of restriction on omnipotence that can be distinguished from some related restrictions. (shrink)