Compatibility with Quote/ BBcode modules?

Can anyone give me any advice on this? FCKeditor puts <p> tags around the input filter messing up its output like this;

<p>[quote=andr&eacute;]</p>
<p>getting in the team may prove difficult if paul has entered as well!!!</p>
<p>[/quote]</p>

Obviously it only affects input filters which have a start and end tag.

Pobster