The Cu-nuclearity is an analogue of Skandalis's K-nuclearity, adopted to the case of Cuntz semigroups of C*-algebras. We prove that this implies nuclearity, and we introduce a weaker form of the condition that may be better adapted for cases where nuclearity is not desirable. We show that the new condition weak Cu-nuclearity, for simple separable C*-algebras, implies exactness and the local lifting property (LLP). This is a joint work with Dan Kucerovsky.