sidebar widget unexpected markup generated

I’m widgetizing my theme. I searched the threads and looked at the Automattic tutorial as well.
Lets come to the point:
Below is my sidebar.php code

<div id="sidebar2">
<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('sidebar2') ) : ?>
  <div id="loerum" class="boxed">
    <h2 class="title"><?php _e('Categories');?></h2>
    <div class="content">
      <ul>
        <?php wp_list_cats('sort_column=name&optioncount=1&hierarchical=0');?>
      </ul>
    </div>
  </div>
<?php endif; ?>
</div>

And this is my function.php

if ( function_exists('register_sidebar') ) {
	register_sidebar(array('name' => 'sidebar2'),
		array('before_widget' => '<div id="%1$s" class="%2$s">',
		'after_widget' => '</div>',
		'before_title' => '<h2 class="title">',
		'after_title' => '</h2>',
	));
}

And this is the markup output:

<div id="sidebar2">
<li id="links" class="widget widget_links"><h2 class="widgettitle">Blogroll</h2>

	<ul>
<li><a href="http://www.alexking.org/">Alex</a></li>
<li><a href="http://inphotos.org/">Donncha</a></li>
<li><a href="http://dougal.gunters.org/">Dougal</a></li>
<li><a href="http://photomatt.net/">Matt</a></li>
<li><a href="http://zengun.org/weblog/">Michel</a></li>
<li><a href="http://zed1.com/journalized/">Mike</a></li>

<li><a href="http://boren.nu/">Ryan</a></li>

	</ul>
</li>
</div>

But this is not the markup output that I want to have.
Below is the markup that I want to get generated.

<div id="sidebar2">
<div id="links" class="boxed">
<h2 class="title">Blogroll</h2>
<div class="content">
<ul>
<li><a href="http://www.alexking.org/">Alex</a></li>
<li><a href="http://inphotos.org/">Donncha</a></li>
<li><a href="http://dougal.gunters.org/">Dougal</a></li>
</ul>
</div>
</div>

Is there anything wrong in my functions.php or sidebar.php?
Thanks.