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Selective Huffman coding has recently been proposed for efficient test- data compression with low hardware overhead. In this paper, we show that the already proposed encoding scheme is not optimal and we present a new one, proving that it is optimal. Moreover, we compare the two encodings theoretically and we derive a set of conditions which show that, in practical cases, the proposed encoding always offers better compression. In terms of hardware overhead, the new scheme is at least as low-demanding as the old one. The increased compression efficiency, the resulting test-time savings, and the low hardware overhead of the proposed method are also verified experimentally.