The capacity of the AWGN broadcast is achieved by superposition coding, but superposition of individual coded modulations does not in general obey a predefined constellation. We propose a coded modulation broadcast with strict channel input modulation constraint via multilevel coding (MLC). For a degraded broadcast channel, conditions of optimality of the multilevel decomposition of a superposition code are derived. Furthermore, a constructive scheme is proposed that simplifies the superposition multilevel code and facilitates the design process, by reducing the inter-dependencies between the levels of the two component codes, and yet achieves rates very close to the constellation constrained capacity. Simulation results on several modulations verify the operation of the proposed coding scheme at or near the constellation constrained capacity.