Sharing clipboard with a nested X-server (Xephyr or Xnest)

Is there a way to share my clipboard between my main X server and a
nested server running with Xephyr?

Here is my startup for Xephyr:

	Xephyr -screen 1024x768 -dpi 100 :1 &

This question can probably be generalized to: how can I share the X
clipboard between two X servers (just the CLIPBOARD selection is fine
-- I don't need the cut buffer or the PRIMARY selection)?

I run KDE on the main X server and fluxbox inside the Xephyr nested
server. I don't think this matters though.

Note that I've also tried Xnest, and it doesn't work there either.

Cheers,
Raman Gupta