Creating a desktop shortcut to a website

I know how to create the shortcut (drag the URL to the desktop) but this defaults to the webloc icon. How can I change the icon to something more use friendly to help a non computer literate user identify which one she wants?

I have tried dropping a jpeg onto the small glyph next to the location at the top of the Get Info name and the larger image at the bottom just changes to "jpeg" with a generic image.

Does the file have to be specific dimensions for example?