Abstract: The problem of constellation shaping for broadcast transmission in degraded channels remains a challenge. This is especially so when a single source communicates simultaneously with two receivers using a finite dimension constellation. This paper focuses on a practical situation where unicast service to each user is transmitted over broadcast channels. We investigate the optimization of an achievable rate closure region by using non-uniform constellations issued from superimposition of high-rate information on low-rate information and by using a nonequiprobable distribution of the transmitted symbols. The achievable rate region is derived for a two-user additive white Gaussian noise (AWGN) broadcast channel and for finite input pulse amplitude modulation (PAM) constellations. A noticeable shaping gain up to 3.5 dB maximum was shown on signal-to-noise ratio (SNR), compared with the equiprobable distribution of transmitted symbols obtained for a 4-PAM constellation when achievable rates are maximized over the probability distribution of channel input signals and the constellation shape.