RFID tags and chips for RFID tags are capable of being inventoried in one or more early attempts. These tags are capable of then refraining from participating in one or more subsequent inventorying attempts. In some embodiments refraining is performed solely by the tag, while in others it is guided by the RFID reader. In some embodiments, an inventoried indicator in the tag becomes updated upon backscattering. The updated value is used by the tag to recognize a subsequent attempt, and thus refrain from participating in it. This permits the subsequent attempt to be used more intensively for inventorying the more elusive, harder-to-read tags, especially in more demanding scenarios.