How can I customize a specific node in Drupal 6 WHEN a custom template has already been applied to the node's content type?

Question

[For Drupal 6] Let's say I've created a content type called "my_content_type". I can override the default template for that entire content-type by creating "page-node-my_content_type.tpl.php". But, what would be the best way to then further customize a single node of that content type (e.g., node 5555)?

I tried the following, but none worked:

• page-node-5555.tpl.php
• page-node-my_content_theme-5555.tpl.php
• node-5555.tpl.php

None of these work. They all continue to use my original content-type template.