One of the major challenges to integrate the wireless LAN technology into portable devices is the limited battery life. The IEEE 802.11e introduced an advanced architecture to improve 802.11 power saving mechanism, named Scheduled Automatic Power Save Delivery (S-APSD). In S-APSD, the access point negotiates periodical schedules with wireless Stations (STA) to deliver buffered traffic and thus prevents the need to poll for each frame by STAs. In S-APSD, in order to reduce wastage of energy, the AP has to avoid overlapping of Service Periods (SPs). Based on existing scheduled events (SEs), the OAS-APSD (Overlapping Aware S-APSD) and LCS-APSD (Low Complexity S-APSD) were proposed to incrementally select the Service Start Times (SSTs) for the new joining traffic streams (TSs) to minimize the chance of SP overlapping. However, in this scheduling fashion, the resulted power saving performance depends on the joining order of TSs and thus may be unsatisfactory. Therefore, our idea is to rearrange the relative offsets of existing SEs to enlarge the system minimum distance. From numerical results, we find that the proposed scheduling algorithms can provide better power saving.