help needed with desktop cleanup

Perhaps I can be a little clearer. I have a working script which downloads files to students, sets all our defaults and throws away old work cluttering up the desktop. I now would like to do the equivalent of hitting the menu item view/cleanup desktop. I have tried cleanup, clean up and also get menu items, but none of it works. Can anyone help a newbie with a snippet of script ( or automator action) to make desktop cleanup work?

Model: G4
AppleScript: 1.10.3
Browser: Safari 417.8
Operating System: Mac OS X (10.4)