List Parents, Children and Grandchildren in nested list

My site structure is something like this:

* Home
* Employees
** Design
*** Designer 1
*** Designer 2
** Engineering
*** Engineer 1
*** Engineer 2
*Contact Us

I want to show a nested menu of subpages in my template.

For example, when viewing the Employees page, the menu should show:
* Employees
** Design
** Engineering

When viewing the Design page, the menu should show:
* Employees
** Design
*** Designer 1
*** Designer 2
** Engineering

When viewing the Designer 1 page, the menu should remain the same.

This is what I have so far. It’s getting there, but I’m stuck now 🙁

<?php
  if($post->post_parent) {
  $children = wp_list_pages("title_li=&child_of=".$post->post_parent."&echo=0");
  $titlenamer = get_the_title($post->post_parent);
  $titlelink = get_permalink($post->post_parent);
  }
  else {
  $children = wp_list_pages("title_li=&child_of=".$post->ID."&echo=0");
  $titlenamer = get_the_title($post->ID);
  $titlelink = get_permalink($post->ID);
  }
  if ($children) { ?>
	<ul id="subnav">
		<li><a class="parent_page_item" href="<? echo $titlelink ?>"><? echo $titlenamer ?></a></li>
		<?php echo $children; ?>
	</ul>
<?php } ?>