In RFID systems, the privacy problem has attracted increasing attention as the tags have extremely limited on-chip resources and may blindly respond to unauthorized readers. One widely used solution is to deploy one or more blocker tags to collide the RF signal sent from protected tags all the time. We in this paper investigate tag identification in privacy-sensitive RFID systems when we have the authorized reader(s). The tag identification under the blocker environment becomes more challenging since the protected tags and blocker tags will always respond concurrently, leading to unreconciled collisions. Therefore, we propose three tag identification protocols IIP, SIP and SUIP, which meet three application requirements: privacy, accuracy, and efficiency. IIP iteratively deactivates blocking tags as well as labeling genuine tags, and finally identifies tags by avoiding all the unreconciled collisions. SIP further avoids the slot waste by carrying out a filter to separate genuine tags from others in advance. Furthermore, SUIP separates the incremental unknown tags from others by using a filter with improved performance and proposes a collision reconciliation technique to accelerate the identification process. Simulation results demonstrate that our protocols are able to guarantee any identification accuracy in a privacy-protected way.