Index tags for specific posts (including custom)

The following code currently indexes all tags for my site (whether attached to a standard post or a custom post) like so...

http://www.furthereast.com/index/

I want to limit this code to index tags from only a specific custom post (and then taxonomy within that custom post) but I cannot work out what adjustment I need to the initial code (I don't know how to set the $args and I suspect I cannot use get_terms() for custom posts). Would appreciate some help.

    $list = '';
$tags = get_terms( 'post_tag' );
$groups = array();
if( $tags && is_array( $tags ) ) {
    foreach( $tags as $tag ) {
        $first_letter = strtoupper( $tag->name[0] );
        $groups[ $first_letter ][] = $tag;
    }
    if( !empty( $groups ) ) {
        foreach( $groups as $letter => $tags ) {
            $list .= "\n" . '<div class="index-letter">' . apply_filters( 'the_title', $letter ) . '</div>';

            foreach( $tags as $tag ) {
                $url = attribute_escape( get_tag_link( $tag->term_id ) );
                $count = intval( $tag->count );
                $name = apply_filters( 'the_title', $tag->name );
                $list .= "\n" . '<li><a href="' . $url . '">' . $name . '</a> (' . $count . ')</li>';
                }
            $list .= "\n" . '</li>';
        }
    }
}else $list .= "\n" . '<p>Sorry, but no tags were found</p>';?>