A myriad of applications such as radio frequency identification (RFID) and smart card networks are emerging in which nodes are designed for extremely low-cost, large scale applications such that the replacement of batteries is not feasible. Energy conservation therefore becomes a major constraint. Classical access protocols are either not energy conserving or lead to unacceptable delays. rn a previous work we proposed three new classes of energy-conserving access protocols designed to minimize delay while drastically reducing the energy required at the mobile node. In this paper, we propose an extension to one of those protocols which greatly reduces the worst case delay experienced by the packets.