HTMLPurifier strips child tags of invalid tags

This is a support request, but I've identified the fix for my case.

I copied some content from another CMS, and the links in an article disappeared. The format of the article was,

<blockquote>Blah blah</blockquote>
<li><a href="http://drupal.org/">blah</a></li>
<li><a href="http://google.com/">blah</a></li>
<blockquote>Blah.</blockquote>

HTMLPurifier removed the child elements of the <li> tags, which removed the links, leaving only their text. The <li>s were removed because they lacked a parent <ul> or <ol>.

This is not specific to the Drupal module - you can see the same by pasting the above HTML at http://htmlpurifier.org/demo.php - but I'd like to know if we can configure HTMLPurifier via the Drupal interface to correct the parent errors without punishing the children.

Think of the DOM children!