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In 1986, Don Knuth published a very simple algorithm for constructing sets of bipolar codewords with equal numbers of Â¿1Â¿s and Â¿-1Â¿s, called balanced codes. Knuth's algorithm is well suited for use with large codewords. The redundancy of Knuth's balanced codes is a factor of two larger than that of a code comprising the full set of balanced codewords. In this paper, we will present results of our attempts to improve the performance of Knuth's balanced codes.