I found a solution, though not as elegant as for what I was searching.
In the template I added some php conditional code. If the template senses a user id, it surrounds the top level menu with a div and id. Then I set up a CSS rule "display:none" applied to that menu item when it is found within that id.
This is not ideal, but it is a workable solution.
in index.php...<?php $my =& JFactory::getUser();
if ( !$my->id ) {echo '<div id="registeredVisitor">';} ?>
...menu code...
<?php if ( !$my->id ) {echo '</div>';} ?>
in template.css...div#registeredVisitor li.item39 {display:none;}