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Reseeding is used to improve fault coverage of pseudo-random testing. The seed corresponds to the initial state of the PRPG before filling the scan chain. In this paper, we present a technique for encoding a given seed by the number of clock cycles that the PRPG needs to run to reach it. This encoding requires many fewer bits than the bits of the seed itself. The cost is the time to reach the intended seed. We reduce this cost using the degrees of freedom (due to don't cares in test patterns) in solving the equations for the seeds. We show results for implementing our technique completely in on-chip hardware and for applying it from a tester. Simulations show that with low hardware overhead, the technique provides 100% single-stuck fault coverage. Also, when compared with conventional reseeding from an external tester or on-chip ROM, the technique reduces seed storage by up to 85%. We show how to apply the technique for both LFSRs and CA.