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We present a pinpoint test set relaxation method for test compression that maximally derives the capability of a run-length encoding technique such as Golomb coding or frequency-directed run-length (FDR) coding. Before encoding a given set of test patterns, we selectively relax some specified bits of the test patterns. By changing a specified bit with value 1 to a don't-care, two consecutive runs of 0s in the test sequence can be concatenated into a longer run of 0, thereby facilitating run-length coding. This procedure retains the fault coverage of the test set. Since the increase in compression depends on the lengths of the two runs that are concatenated with each bit relaxation, a lookup table, referred to as the gain table, is pre-computed and used during the test set relaxation procedure to maximize the likelihood of increasing the amount of test data compression. The gain table is used to pinpoint the bit positions with value 1, which when relaxed to don't-cares, will yield the most compression. In this way, the given test pattern set is appropriately modified as a preprocessing step before test compression. Experimental results for the ISCAS benchmark circuits show that the proposed method can be used to increase the effectiveness of run-length coding methods for test data compression.