In this paper, adaptive lossy coding procedures are applied to 12 bit/pixel lung radiograms, with the general goal to achieve high compression ratios while preserving the diagnostic information. To grant the diagnostic accuracy, regions that are classified as significant from a pathological point of view, have been preserved in the coding process. The extraction of relevant regions (nodules) has been performed automatically by the use of suitable operators based on mathematical morphology. Image structures, are classified in different categories, to treat the `generic' ones, peculiarly bony structures prevailing in this kind of images, differently from those having a diagnostic interest, because joined to specific pathologies. The last version of the JPEG sequential coding scheme, that allows variable quantization, has been used to code the images. This procedure is based on the DCT transform applied to 8 X 8 image blocks followed by adaptive quantization of the transformed blocks and then by an entropy coding of the quantized coefficients. As the information loss is due to the quantization operation, blocks containing `interesting' structures are quantized using smaller steps.