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We Propose An Algorithm For Encoding Quantized Post-interpolation Residuals Within The Framework Of Hierarchical Image Compression. This Coding Algorithm Is Based On A Hierarchical Representation Of The Plain Areas Of Quantized Post-interpolation Residuals To Improve The Coding Efficiency Of These Areas. The Proposed Algorithm Reorders The Post-interpolation Residuals To Increase The Size Of The Plain Areas. We Embed The Proposed Coding Algorithm For Post-interpolation Residuals Into A Hierarchical Image Compression Method. This Method Is Based On Interpolation The Image Scale Levels Using More Resampled Scale Levels Of The Same Image. The Errors Of This Interpolation (post-interpolation Residuals) Are Then Quantized And Encoded. We Use The Proposed Algorithm To Encode The Quantized Post-interpolation Residuals Of The Hierarchical Compression Method. We Perform Computational Experiments To Study The Effectiveness Of The Proposed Algorithm For A Set Of Natural Images. We Experimentally Confirm That The Use Of The Proposed Coding Algorithm For Post-interpolation Residuals Makes It Possible To Increase The Efficiency Of The Hierarchical Method Of Image Compression.