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This work describes a general method of testing for redundancies in the sign lists of ancient scripts by data mining the positions of the signs within the inscriptions. The redundant signs are allographs of the same grapheme. The method is applied to the undeciphered Indus Valley Script, which stands out from other ancient scripts by having a large proposed sign list that contains dozens of asymmetric signs that have mirrored pairs. By a statistical analysis of mirrored asymmetric signs, this paper shows that the Indus Valley Script was multi-directional and the mirroring of signs often denotes only the direction of writing without any difference in meaning. For this and five other specific reasons listed in the paper, 50 pairs of signs, 23 mirrored, and 27 non-mirrored, can be grouped together because each pair consists of only insignificant variations of the same original sign. The reduced sign list may make decipherment easier in the future.