Allow gzip in zlib port (or steps to implement it)

I am currently writing an API giving back JSON data that may be highly redundant, and I wish to offer users the standard `Content-Encoding`s available.

Thanks to the Zlib C++ port included now in Beast, I have successfully allowed `Content-Encoding: deflate`.
However, I wish to also offer `Content-Encoding: gzip`, especially since not every web client allows deflate.
So my real question boils down to this: What would it take to port the gzip part of zlib into the Inflate/Deflate streams (beside the obvious window bits +16) ?

This is mainly for my personal project, but I would argue that such a facility would be great in Beast so that people who wish to serve compressed HTTP bodies could do so in gzip just as easily as in deflate, given the C Zlib has support for both already.