In the promising high-speed differentiated-services (diffserv) wireless broadband networks specifically 802.16 standard, bandwidth scheduling algorithms play important role in providing the Quality-of-Service (QoS) guarantees required by many applications. Most of the research is focused on packet scheduling, but it is not clear yet which scheduling algorithms will work best with 802.16. Our scheme is a refined version of the modified Deficit Round Robin (MDRR) technique proposed by Fattah and Leung. We modify the redistribution strategy of MDRR to achieve better performance in terms of delay, throughput and fairness, and analyze the performance of our scheme via exhaustive packet-level simulations, under realistic wireless scenarios. In this paper, a new scheduling discipline called Customized Deficit Round Robin (CDRR) is presented, while preserving the simplicity available in the original DRR design which is fair, efficient and in addition has a low latency bound. The performance of our scheme is compared with MDRR using the OPNET simulator. The comparison is carried out, by investigating the latency and bandwidth sharing properties of the algorithms.