TinyMCE and the awful code it produces

So here I am, happily pasting content from my Wordpress site into Notepad, and then into Drupal when I notice that a story that I published loses it's bold formatting.

"What?" I say to myself. "Why doesn't this work? I'm using filtered html, which should let the strong HTML element through."

No dice. TinyMCE, for some reason, has made my bolds using the B tag, which is verboten in Filtered HTML. Now, I know that I could easily just allow the B tag to be used in Filtered HTML, but you know, I'd rather use strong. Oh, and also my paragraphs are just separated by BR's instead of being enclosed in P tags!

I searched here, and then went into TinyMCE's configuration file and added

$plugins['xhtml_helper'] = array();
$plugins['xhtml_helper']['theme_advanced_buttons1'] = array('helper');

to the config file in the hopes that that would somehow enable the editor to do what I wanted, but no such luck.

I loaded FCKEditor and found the same problem.

Anybody run into this?