Trying to hook into the function comment_text() supplied by Wordpress API to wrap the output of every comment into a <div>...</div> container I am running into the following problem:

Without my added filter the output of comment_text() looks like this:

<p>Hello User!</p>
<p>Thank you for your comment.</p>
<p>Stefan</p>

Thats fine but as I said I would like to have it wrapped into a <div class="comment-text">...</div>. As far as I know the correct way doing this would be in adding a filter to functions.php of my theme and so I did:

function stefan_wrap_comment_text($content) {
    return "<div class=\"comment-text\">". $content ."</div>";
}
add_filter('comment_text', 'stefan_wrap_comment_text');

As I can see from the output the given filter works but it has a negative sideeffect to the first paragraph of the content as you can see in the following example. The first paragraph should be <p>Hello User!</p> but looks like this: Hello User!.

<div class="comment-text">
    Hello User!
    <p>Thank you for your comment.</p>
    <p>Stefan</p>
</div>

Any ideas or hints what I am doing wrong?