It is possible to improve the features supported by devices with embedded systems by increasing the processor computing power, but this always results in higher costs, complexity, and power consumption. An interesting alternative is to use the growing networking infrastructures to do remote processing and visualization, with the embedded system mainly responsible for communications and user interaction. This enables devices to behave as if much more “intelligent” to users, at very low costs and power. In this article we explain how compression can make some of these solutions more bandwidth-efficient, enabling devices to simply decompress very rich graphical information and user interfaces that had been rendered elsewhere. The mixture of natural images and video with text, graphics, and animations simultaneously in the same frame is called compound video. We present a new method for compression of compound images and video, which is able to efficiently identify the different components during compression, and use an appropriate coding method. Our system uses lossless compression for graphics and text, and, on natural images and highly detailed parts, it uses lossy compression with dynamically varying quality. Since it was designed for embedded systems with very limited resources, and it has small executable size, and low complexity for classification, compression and decompression. Other compression methods (e.g., MPEG) can do the same, but are very inefficient for compound content. High-level graphics languages can be bandwidth-efficient, but are much less reliable (e.g., supporting Asian fonts), and are many orders of magnitude more complex. Numerical tests show the very significant gains in compression achieved by these systems.