wired Mighty Mouse: can I close a window with a simple click?

For years I could depress the scroll wheel on my Logitech mouse to simply close the open active window. That was great.

Now I just bought a 24" iMac, and I can't (it seems) use the Logitech to close windows via an aimless click, plus some other problems. So I am using the A1152 wired Apple Mighty Mouse that came with the iMac. I just learned (with difficulty) how to right click it, etc.

Question: can it be programed or customized to simply close an active window with a click, anywhere -- just by the click? (I am not talking about using the Command-W keyboard stroke, or clicking the little red dot of the window.)

Thanks.