Certain aspects of the present disclosure provide methods and apparatus for using a random offset to achieve power savings. For certain aspects, a Basic Service Set (BSS)-specific offset may be added to the (partial) association identifier (AID) prior to entering the partial AID into a 9-bit field of the physical layer (PHY) header (e.g., bits 13-21 of the NSTS field). The BSS-specific offset may be selected randomly by an access point (AP) and signaled to the associated stations (STAs) through the association response, or the offset may be communicated to the STA via other means. In this manner, the value in the 9-bit field for downlink transmissions may, with high likelihood, be different from one BSS to the next, allowing STAs to remain awake only when a frame is being transmitted to them.