The answer is actually fairly long and involved, but there is a great blog post that explains the steps (with screenshots) for taking control of this issue and getting it right. The article assumes you're running the Nvidia driver, which if you aren't, you might have some trouble ... but ... from the look of it, it should work with any driver.
This is the article
In a nutshell, you want to run
winecfg, enable a virtual desktop, then use the
xdotool command (installing the package if necessary) to move the window to the correct screen.
By the way, I think you can avoid using
xdotool if you run Kwin window manager because it has extremely flexible configuration of where to place windows and how big to make them, but since you're running Compiz I doubt you're running KDE right now.