A new lossless test vector compression scheme is presented which combines linear feedback shift register (LFSR) reseeding and statistical coding in a powerful way. Test vectors can be encoded as LFSR seeds by solving a system of linear equations. The solution space of the linear equations can be quite large. The proposed method takes advantage of this large solution space to find seeds that can be efficiently encoded using a statistical code. Two architectures for implementing LFSR reseeding with seed compression are described. One configures the scan cells themselves to perform the LFSR functionality while the other uses a new idea of "scan windows" to allow the use of a small separate LFSR whose size is independent of the number of scan cells. The proposed scheme can be used either for applying a fully deterministic test set or for mixed-mode built-in self-test (BIST), and it can be used in conjunction with other variations of LFSR reseeding that have been previously proposed to further improve the encoding efficiency.