Abstract-The main disadvantage of LFSR-based compression is that it should be usually combined with a constrained ATPG process, and, as a result, it cannot be effectively applied to IP cores of unknown structure. In this paper, a new LFSR-based compression approach that overcomes this problem is proposed. The proposed method allows each LFSR seed to encode as many slices as possible. For achieving this, a special purpose slice, called stop-slice, that indicates the end of a seed's usage is encoded as the last slice of each seed. Thus, the seeds include by construction the information of where they should stop and, for that reason, we call them self-stoppable. A stop-slice generation procedure is proposed that exploits the inherent test set characteristics and generates stop slices which impose minimum compression overhead. Moreover, the architecture for implementing the proposed technique requires negligible additional hardware overhead compared to the standard LFSR-based architecture. The proposed technique is also accompanied by a seed calculation algorithm that tries to minimize the number of calculated seeds.