Is this only happening in mod_html? or does all the modules on your site display the same space between header and module contents?
You could add some CSS to your template. If you have the Firebug extension for Firefox, you can easily view the CSS related to the above, and modify it in Firebug to get a live view of the changes. Then add those CSS changes to your template.
Firebug:
http://www.getfirebug.com/
