Here is what desktop shortcuts look like without tile backgrounds (actually, transparent tiles). This allows you to get shortcuts closer together, while still looking nice and not interfering with one another. I've also attached two shortcut tile backgrounds I made by modding the original background tile from the default theme, along with the circuit board wallpaper if you would like to use it. I just copy the tile I want to the relevant theme images directory and overwrite the existing file (after making a backup):
/user/share/themes/YOURTHEME/images/ApplicationShorcutApplet.png
One tile in the .zip is the transparent tile, while the other is a simple wire frame with a transparent center.
After replacing the existing ApplicationShortcutApplet.png, just reboot or switch to a different theme and then back to see the changes.