Check for header image before showing it, in Twenty Ten. props koopersmith, see #14486 for trunk.

git-svn-id: https://develop.svn.wordpress.org/trunk@15520 602fd350-edb4-49c9-b593-d223f7449a82

wp-content/themes/twentyten/header.php

@@ -73,7 +73,7 @@
 							$image[1] >= HEADER_IMAGE_WIDTH ) :
 						// Houston, we have a new header image!
 						echo get_the_post_thumbnail( $post->ID, 'post-thumbnail' );
-					else : ?>
+					elseif ( get_header_image() ) : ?>
 						<img src="<?php header_image(); ?>" width="<?php echo HEADER_IMAGE_WIDTH; ?>" height="<?php echo HEADER_IMAGE_HEIGHT; ?>" alt="" />
 					<?php endif; ?>
 			</div><!-- #branding -->