Screen and Cygwin: no tab completion?

I'm having some problems working with my development environment. Specifically, after I invoke the screen utility from within Cygwin I lose the ability to do tab completion. Before I invoke screen however tab completion works just fine.

I messed around with setting different values for the TERM env variable (VT100, xterm etc) but without success. It must be something trivial but I have no idea anymore. Does StackOverflow have any suggestions for me?