Code decompositions (a.k.a code nestings) are used to design good binary polar code kernels. The proposed kernels are in general non-linear and show a better rate of polarization under successive cancelation decoding, than the ones suggested by Korada et al., for the same kernel dimensions. In particular, kernels of sizes 14, 15 and 16 are constructed and shown to provide polarization rates better than any binary kernel of such sizes.