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The instantaneous side of information source code (SISC) design is considered. In the SISC configuration, the encoder describes source X to the decoder; the decoder uses this description and side information Y, to reconstruct X. Prior work on lossless and near-lossless SISC design demonstrates that globally optimal design is NP-hard. A family of polynomial complexity code design algorithms is introduced that approximates the optimal solution for lossless and near-lossless SISCs. The algorithm may be used to design both Huffman and arithmetic SISCs for an arbitrary probability mass function p(x,y). Experimental results comparing the resulting performances to each other and to the theoretical limit are included.