Displaying recent comments from only one post

I’m trying to display only the 20 most recent comments of each post in the comment section.

I can’t use comment pagination, as I’m working with an old version of WordPress and have already tweaked a lot the theme, so updating it could be risky.

So far all I have this code int the functions.php file, that displays the 20 most recent comments from the whole blog:

< ?php // Get Recet Comments Function
function dp_recent_comments($no_comments = 10, $comment_len = 35) {
    global $wpdb;
	$request = "SELECT * FROM $wpdb->comments";
	$request .= " JOIN $wpdb->posts ON ID = comment_post_ID";
	$request .= " WHERE comment_approved = '1' AND post_status = 'publish' AND post_password =''";
	$request .= " ORDER BY comment_date DESC LIMIT $no_comments";
	$comments = $wpdb->get_results($request);
	if ($comments) {
		foreach ($comments as $comment) {
			ob_start();
			?>
				<li>
					<a href="<?php echo get_permalink( $comment->comment_post_ID ) . '#comment-' . $comment->comment_ID; ?>">< ?php echo dp_get_author($comment); ?>:</a>
					< ?php echo strip_tags(substr(apply_filters('get_comment_text', $comment->comment_content), 0, $comment_len)); ?>
				</li>
			< ?php
			ob_end_flush();
		}
	} else {
		echo '<li>'.__('No comments', 'banago').'';
	}
}
function dp_get_author($comment) {
	$author = "";
	if ( empty($comment->comment_author) )
		$author = __('Anonymous', 'banago');
	else
		$author = $comment->comment_author;
	return $author;
}?>

Can you please help me turn it into a post-aware code, so that it displays only the 20 most recent comments from one post? Thanks in advance!