In this paper, we present a new test data compression scheme for multi-scan designs to reduce the test data volume and thus the test cost. The proposed method achieves the target in two steps. First a drive bit matrix with less columns is generated by exploiting the compatibilities between the columns of the initial scan bit matrix, as well as the inverse compatibilities and the logic dependencies between the columns of the mid bit matrices. Then a dictionary bit matrix with limited rows is constructed, having the properties that for each row of the drive bit matrix a compatible row exists or can be generated by an XOR operation on multiple rows in the dictionary bit matrix, and the total numbers of rows in the dictionary bit matrix used to compute all the compatible rows is minimal. The rows in the dictionary matrix are encoded to further reduce the number of ATE channels and the test data volume. The experimental results for the large ISCAS 89 benchmarks show that the proposed method significantly reduces test data volume for multi-scan designs.