pasting primary X selection into Emacs

[mandar . mitra]

I would like to use C-y or <middle button> to yank the primary X
selection in Emacs.

C-y and middle button both work as expected after a kill (since the
kill updates the primary selection), but if I use the mouse to create a
new primary selection after that, and then do a C-y, I still get the
last killed text, instead of the new primary selection.

Is there some way to yank whichever is more recent: the last killed
text or the primary selection?

Thanks for any pointers,
Mandar.

ps 1: I've looked at some of the discussion on cutting and pasting
between Emacs and X11 apps, but
haven't found the answer to this particular question.

ps 2: I had posted this on comp.emacs, but got no suggestions, so I'm
trying here. I should have crossposted at the outset. Sorry.