Simon Fell points to an article showing how to add HTTP 1.1 compression support to a .NET web service client proxy.

Yasser Shohoud reports that "IIS 6.0 makes it easy to compress replies including Web services replies. In .NET 2.0, the client will automatically tell the server that it accepts gzip compression and it will automatically decompress replies. [...] Note that we don't have a client side compression feature so if you are sending Base64 data from the client and you want to compress it, you would need to use 3rd party compression library or roll your own." (emphasis mine)