The emerging international standard for compression of bilevel images and bilevel documents, JBIG2, provides a mode dedicated for lossy coding of halftones. The encoding procedure involves descreening of the bilevel image into gray scale, encoding of the gray-scale image, and construction of a halftone pattern dictionary. The decoder first decodes the gray-scale image. Then for each gray-scale pixel the decoder looks up the corresponding halftone pattern in the dictionary and places it in the reconstruction bitmap at the position corresponding to the gray-scale pixel. The coding method is inherently lossy and care must be taken to avoid introducing artifacts in the reconstructed image. We describe how to apply this coding method for halftones created by periodic ordered dithering, by clustered dot screening (offset printing), and by techniques which in effect dithers with blue noise, e.g., error diffusion. Besides descreening and construction of the dictionary, we address graceful degradation and artifact removal.