In this paper, restricted overflow strategy is proposed as a novel channel access strategy for the queueable hierarchical channel structure, which has been proposed as one of "Wideband-ISDN" channel structures. In this policy, overflow from higher bit rate channels to lower bit rate channels is partly restricted by the number of waiting customers in the higher channel's buffer. Therefore, thresholds, which restrict overflow, are considered on the buffer. First, we present the system model with two types of services and restricted overflow strategy. Next, we provide a queueing analysis of this strategy. After that, some numerical results of both conventional overflow strategy and restricted overflow strategy are presented, and we compare the average holding times under these strategies. Finally, we show that, if we choose appropriate thresholds, the average holding time of higher level traffic is improved.