In this work we study the effect of hierarchical modulation on completion time minimization in wireless broadcast channels. The time needed to transmit all bits intended for a particular user is defined as its completion time. In this work we investigate minimizing the maximum completion time over all users in the broadcast channel. We compare time division, opportunistic scheduling, and 3 different adaptive modulation schemes. Depending on how fast the channel conditions change, the new rate adaptive hierarchical modulation scheme can introduce significant gains in minimizing the maximum completion time.