In this paper a new test set embedding method with reseeding for scan-based testing is proposed. The bit sequences of multiple cells of an LFSR, which is used as test pattern generator, are exploited for effectively encoding the test set of the core under test (multiphase architecture). A new algorithm which comprises four heuristic criteria is introduced for efficiently selecting the required seeds and LFSR cells. Also, a cost metric for assessing the quality of the algorithm's results is proposed. By using this metric, the process of determining proper values for the algorithm's input parameters is significantly simplified. The proposed method compares favorably with the most recent and effective test set embedding techniques in the literature.