there's no need to compress already compressed files.
a .gz file is already compressed, with the same algo it would be used by the http-compression (that is zlib).
i don't know why your software is saying you are downloading faster, but http-compression is not helping for sure in a gzip file.
mp3, jpg, pdf, etc already use optimized compression that gets better results than http-compression.
http-compression has been introduced to help transfering text based files.
trying to compress a 10MB mp3 before sending it is just a waste of CPU.