Show other posts in same two categories

I found code by MichaelH from ten months ago on this post which almost does exactly what I want. It shows related post titles (excluding the current post) that are in the same category as the current post, or if there are none it does nothing. What I want to do is make it work on two categories so if the other posts are in the same two categories as the current post, show them.

If it matters, my posts always belong to children of two parent categories.

Here’s his original code:

<?php
if ( is_single() ) {
  $cats = wp_get_post_categories($post->ID);
  if ($cats) {
    $first_cat = $cats[0];
    $args=array(
      'cat' => $first_cat,
      'post__not_in' => array($post->ID),
      'showposts'=>5,
      'caller_get_posts'=>1
    );
    $my_query = new WP_Query($args);
    if( $my_query->have_posts() ) {
      echo 'Related Posts';
      while ($my_query->have_posts()) : $my_query->the_post(); ?>
        <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></p>
       <?php
      endwhile;
    } //if ($my_query)
  } //if ($cats)
  wp_reset_query();  // Restore global post data stomped by the_post().
} //if (is_single())
?>

I haven’t been able to find any plugins or other posts on WP that do this. I did find another snippet but it is based on query_posts and I just want to show linked titles:

<?php query_posts(array('category__and'=>wp_get_post_categories($post->ID))); ?>

Thanks for any help here. I’m not much of a coder but I have spent a few hours researching this, so I’m not lazy just not talented. ??