One important problem concerning incommensurability is how to explain that two theories which are incommensurable and therefore mutually untranslatable and incomparable in a strictly logical, point-by-point way are still competing. The two standard approaches have been to argue either that the terms of incommensurable theories may share reference, or that incommensurable theories target roughly the same object domain as far as the world-in-itself is concerned. However, neither of these approaches to the problem pay due respect to the incommensurability thesis' insights. In this paper I shall first show the inconsistency between the basic premises underlying Kuhn’s incommensurability thesis and the two standard responses to the thesis. I shall then argue that if one adopts Kuhn’s position, the response must build on a notion of overlap between phenomenal worlds. Finally, I shall argue that overlap between complex structures of features can provide the basis for such a notion, and that this makes it possible to explain how incommensurable theories may compete.