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Compound images are combinations of text, graphics and natural images. They possess characteristics different from those of natural images, such as a strong anisotropy, sparse color histograms and repeated patterns. Former research on compressing them has mainly focused on developing certain strategies based on some of these characteristics but has failed so far to fully exploit them simultaneously. In this paper, we investigate the combination of four up-to-date strategies to construct a comprehensive scheme for compound image compression. We have implemented these strategies as four types of modes with variable block sizes. Experimental results show that the proposed scheme achieves significant coding gains for compound image compression at all bitrates.