Found the solution for this issue:
We use the Microsoft TMG as a Proxy in our company and it seems to remove the "Content-Encoding" header (and other magic stuff). I was confused because some pages like twitter.com are served to my PC with the "content-encoding: gzip" header and other without any "Content-Encoding" header.
My wild guess: The TMG is case sensitive and only looks for "Content-Encoding", that's why I receive some requests with it and some without it.
So - compression with the correct header works as expected.