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Given a high resolution compressed video stream this paper looks at the problem of extracting video from a small window at an arbitrary, but static location, in compressed form, without having to either decode the high resolution video stream or encode the window stream. Since state of the art video compression algorithms use motion compensation in one form or the other, the compressed video stream cannot be parsed to obtain the window stream without decoding the high resolution stream to some extent and subsequent re-encoding. On the other hand storing all possible windows as separate streams on the server is clearly infeasible, at least as of today, as it would lead to an explosion of the storage space requirement. It is shown that with a comparatively small increment in the server's storage requirement, it is possible to obtain compressed window streams out of the high resolution stream with minimal parsing, no decoding or re-encoding and little quality loss. Furthermore, methods to trade off the space required on the server with the compression efficiency of the window stream are shown. Experimental results obtained from applying the proposed method on MPEG-2 compressed video sequences are also provided.