An efficient encoding scheme based on an improved Laplacian pyramid is proposed for lossless/lossy compression aimed at archival and progressive transmission of grayscale medical images. The major assets are: pyramid entropy is decreased by adopting two different filters for reduction and expansion; encoding priority is given to major details through a hierarchical content‐driven decision rule; the binary quad‐tree of split/unsplit nodes is blockwise zig‐zag scanned and run‐length encoded. Error feedback along the levels of the Laplacian pyramid ensures control of the maximum absolute error, up to fully reversible reconstruction capability, and enhances the efficiency and the robustness of the whole scheme. While coding results on the standard greyscale image Lena are pretty competitive with the most recent literature, reversible compression of scanned RX images achieves ratios of about 1:5, establishing improvements over DPCM schemes; high‐quality lossy versions at 0.15 bit/pel outperform JPEG both visually and quantitatively. Moreover, no floating‐point computation is required in the algorithm, and on‐line compression and reconstruction are feasible on general‐purpose terminals.