Emacs hangs on X11 paste--how to diagnose?

[jrw]

I've been having a problem in Emacs (my own build based on 24.4.51.1) where 
sometimes, if I try to paste from an X11 program, either using C-y or a middle 
click, Emacs freezes for several seconds.  Pressing C-g does nothing, but 
usually Emacs starts responding again after a few seconds.  Since I can't 
reproduce the issue reliably, does anyone have any ideas on how to diagnose 
this problem.  It seems like the next step may be to run Emacs in gdb, but I'd 
like to avoid that if possible.