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There are two key aspects affecting the performance of butterfly network with wireless network-coded relaying. The first one is the amount of Complementary Side Information (C-SI) at destinations and the second is given by a parametric Multiple-Access channel performance of source constellation alphabets. In this paper we show that theNon-uniform 2-slot (NuT) constellations, proposed originally for bi-directional relaying in the 2-Way Relay Channel (2-WRC), are suitable also for the butterfly network, combining the favorable parametric channel performance with the potential to increase the reliability of required C-SI (necessary for successful decoding at the final destination). Possessing both these qualities, the NuT alphabets surpass again the conventional linear modulation schemes, extending further the scope of their potential application.