Two new renormalization schemes for conductivity upscaling in heterogeneous media are presented. The schemes follow previous ones by performing the renormalization over square cells of size 2(d) with d being the dimensionality. Contrasting with previous schemes, the two-dimensional scheme makes use of the exact 2 x 2 block-conductivity. On the basis of the structure of the exact two-dimensional block-conductivity, an analogous three-dimensional scheme is proposed. The new schemes are tested on a number of benchmark problems and are shown to be significantly more accurate than existing schemes.