In this paper, maximal achievable rate regions are derived for power constrained AWGN broadcast channel involving nite constellations and two users. The achiev- able rate region is studied for various transmission strategies including superposi- tion coding and compared to standard schemes such as time sharing. The maxi- mal achievable rates are obtained by optimizing over both the joint distribution of probability and over the constellation symbol positions. A numerical solution is pro- posed for solving this non-convex optimization problem. Then, we consider several variations of the same problem by introducing various constraints on the optimiza- tion variables. The aim is to evaluate e ciency vs complexity tradeo s of several transmission strategies, some of which (the simplest ones) can be found in actual standards. The improvement for each scheme is evaluated in terms of SNR savings for target achievable rates or/and percentage of gain in achievable rates for one user compared to a reference scheme. As an application, two scenarios of coverage areas and user alphabets are considered. This study allows to evaluate with practical criteria the performance improvement brought by more advanced schemes.