Binary-exponential sleep mode (BE-SM) operation is an energy-saving solution of mobile stations for best-effort or non-realtime services. In general, there is a trade-off between energy consumption and delay. Especially, in the conventional BE-SM operations, the standard scheme achieves the lower bound of delay, while the threshold scheme achieves the upper bound of delay. Since the threshold scheme yields the highest energy efficiency at the expense of delay, it does not guarantee given quality-of-service (QoS) requirements. From the viewpoint of various QoS requirements, we propose a relaxed QoS (RQ) scheme with relaxed QoS requirements and a stringent QoS (SQ) scheme with stringent QoS requirements in which we have two policies: additional sleep cycles and buffer-threshold. The results show that the proposed RQ scheme has a trade-off between energy efficiency and user satisfaction ratio at low arrival rate, while the proposed SQ scheme is close to the upper bound of energy efficiency while satisfying the stringent QoS requirements.