In this paper, hierarchical modulation is used in conjunction with maximum-weight scheduling to achieve lower transmission delays. Via hierarchical modulation, the scheduled user has the option to transmit to two users simultaneously. In order to reflect service differentiation schemes used in upper layers, a scenario in which each user generates packets with different priority levels is considered. It is assumed that as long as there are high priority packets waiting in the scheduled user's queue, lower priority packets cannot be transmitted. It is shown that, using hierarchical modulation in the presence of packet prioritization, average delay of low priority traffic can be reduced while achieving higher throughput. In the absence of packet prioritization, using hierarchical modulation lowers packet transmission delays without any loss in throughput. The effect of multiple access interference is also investigated. It is shown that both single and two-layer schemes have similar average spatial reuse factors. (C) 2016 Elsevier GmbH. All rights reserved.