This paper proposes a compound image coding method named united coding (UC). In UC, several lossless coding tools such as dictionary-entropy coders, run-length encoding (RLE), Hextile, and a few filters used in portable network graphics (PNG) format are united into H.264 like intraframe hybrid video coding. The basic coding unit (BCU) has a size typically between 16?×?16 pixels to 64?×?64 pixels. All coders in UC are used to code each BCU. Then, the lossless coder that generates minimum bit-rate (R) is chosen as the optimal lossless coder. Finally, the final optimal coder is chosen from the lossy intraframe hybrid coder and the optimal lossless coder using R-D cost based optimization criterion. Moreover, the data coded by one lossless coder can be used as the dictionary of other lossless coders. Experimental results demonstrate that compared with H.264, UC achieves up to 20 dB PSNR improvement and better visual picture quality for compound images with mixed text, graphics and natural picture. Compared with lossless coders such as gzip and PNG, UC can achieve 2---5 times higher compression ratio with just a minor loss and keep partial-lossless picture quality. The partial-lossless nature of UC is indispensable for some typical applications, such as cloud computing and rendering, cloudlet-screen computing and remote desktop, where lossless coding of partial image regions is demanded. On the other hand, the implementation complexity and cost increment of UC is moderate, typically less than 25 % of a traditional hybrid coder such as H.264.