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, the authors call them self-stoppable.