We study the design of a digital video broadcasting - satellite - second generation broadband system in order to maximise spectral efficiency. This task is usually challenging because of channel variability. The solution adopted in modern satellite communications systems relies mainly on a time-sharing strategy. Recently, we demonstrated the advantage of combining time sharing with hierarchical modulation to increase the transmission rate of such systems. However, the optimal spectral efficiency remained an open question. In this paper, we show that the optimal transmission rate is the solution of a linear programming problem. We study the performance of the optimal scheme for interactive satellite services in the context of a digital video broadcasting - satellite - second generation system. Copyright (C) 2015 John Wiley & Sons, Ltd.