a method and system for compressing bitmap data in a system for sharing an application running on a host computer with a remote computer , wherein the shared application &# 39 ; s screen output is simultaneously displayed on both computers . simultaneous display of screen output is achieved by efficiently transmitting display data between the host computer and the remote computer . when a font used by the host computer for displaying text is not available on the remote computer , the host computer sends a bitmap representation of the text for display , rather than the text itself . bitmap representations are cached by the remote computer , so that the same bitmap representation need not be repeatedly transmitted from the host computer to the remote computer . bitmap representations are compressed by the host computer prior to transmission , transmitted , then decompressed by the remote computer .