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Despite their limited wiring, as off-chip connections they can account for a significant amount of the total power consumption of a system-on-chip device. Encoding the information sent on these buses is the most intuitive and affordable way to reduce their power contribution; moreover, the encoding can be made even more effective by exploiting the fact that many embedded applications can tolerate intermediate approximations without a significant impact on the final quality of results, thus trading off accuracy for power consumption. We propose a simple yet very effective approximate encoding for reducing dynamic energy in serial buses. Our approach uses differential encoding as a baseline scheme and extends it with bounded approximations to overcome the intrinsic limitations of differential encoding for data with low temporal correlation. 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