Abstract: Lossless and lossy codes are combined for data compression. In one embodiment, the most significant bits of each value are losslessly coded along with a lossy version of the original data. Upon decompression, the lossless reduced-precision values establish absolute bounds for the lossy code. Another embodiment losslessly codes the leading bits while trailing bits undergo lossy coding. Upon decompression, the two codes are summed. The method preserves edges and other sharp transitions for superior lossy compression. Additionally, the method enables description-length inference using noisy data.