To provide pilots with necessary information to make informed decisions on the avoidance of hazardous weather and to maintain situational awareness of the weather conditions, the FAA is actively developing the capability to provide real-time graphical weather information to aircraft through the use of bandwidth-limited data links such as Mode S. The information content of weather images and the restricted bandwidth of the transmission channel require that the images be extensively compressed. This paper provides the results of a study concerning the applicability of various data compression algorithms to the weather image problem. Its conclusion is that the Polygon-Ellipse Algorithm developed at Lincoln Laboratory provides the best combination of compression, computational efficiency, and image quality for the encoding of weather images over the Mode S data link or other similarly bit-limited data links.