WYSIWYG area won't match Front end styles

I can not get the WYSIWYG area to display the same style as the front end css is set to.

In short, I want <p> to single space everytime. We want to only double space where we intend it to. I have set the css as thus
p {margin-bottom: 0;}
in both the stylesheet for the site and in
editorarea.css.

The WYSIWYG area still show double spacing between paragraphs with a single return/new line/carriage return.

What else do I need to change to get be sure the editor styles match my front end styles?

Thanks