Header markup is always printed even if empty

In the page.tpl.php, the header markup is always printed even if the containing variables are empty is disabled.

In my sub theme, it easy to change this, but it doesn't seem right to have styled, empty divs floating around.

I added this:

<?php if ($logo || !empty($site_name) || !empty($primary_nav) || !empty($secondary_nav) || !empty($page['navigation'])): 

?>

Also note that once the header no longer exists the h1 page-headers require their margin back that is removed in overrides.css

.page-header{margin-top:0}

Maybe there is a better way of overriding the CSS here?