How can I make clicking the scroll wheel on my mouse (ie pressing the scroll wheel like a button) NOT paste.

I find this highly irritating... I'll accidentally click the scroll wheel when scrolling, and then inadvertently paste something into whatever it is I'm working on. It's really bad when I don't notice i've pasted only to discover later that I've ruined a file.

I've checked the GNOME mouse control panel, but don't see any option there to define the behaviour of clicking the middle button/scroll wheel.

Please help!