Many friends complained their compiz didn’t work after upgrading Ubuntu to Gusty(7.10).I searched and searched,finally I got a workable method.It is really a practical method ,as I sorted ATI+compiz+Gusty issues out for my friends by following it:

Make sure you are using the fglrx driver (See System > Administration > Screen and Graphics). Open /etc/X11/xorg.conf in your favourite editor and add the following to Section “Device” Under the Busid Option:

Option “backingstore” “true”
Option “EnablePageFlip” “true”
Option “SubPixelOrder” “none”
Option “AccelMethod” “XAA”
Option “RenderAccel” “true”
Option “AGPMode” “4″
Option “ColorTiling” “on”
Option “DynamicClocks” “on”
Option “mtrr” “on”
Option “VideoOverlay” “on”
Option “OpenGLOverlay” “off”

Check that under the Section “Extensions” that the Option “Composite” is enabled, i.e.:
Section “Extensions”
Option “Composite” “Enable”
EndSection

Finally enable Desktop Effects via System > Preferences > Appearance > Desktop Effects.

This method come from:http://www.djohnson.info/2007/09/01/gutsy-gibbon-and-compiz-on-ati-mobility-radeon/