Thanks Eric. I've already tried the BreakElement property but that hasn't helped. If I understand the documentation, that property is used to determine which tags to insert when Enter is pressed. In my case, I haven't pressed Enter yet, I'm just typing text.
On your example page, I selected "Br" mode and typed the word "TEST" into the Normal view. When I selected HTML view, I saw this:
<p>TEST</p>
And it only happens in IE. That's what I'm trying to stop from happening -- the insertion of the <p> tags.