WordPress Twentyten Theme Without Header Image

The latest version of the Twentyten theme seems to have introduced a bug in the header. If you opt for no header image, you’ll end up with a large space and a broken image icon in your header:

The problem is a conditional in wp-content/themes/twentyten/header.php which writes out an img tag even if get_header_image() returns an empty string:

   // Check if this is a post or page, if it has a thumbnail, and if it's a big one
   if ( is_singular() &&
      has_post_thumbnail( $post->ID ) &&
         ( /* $src, $width, $height */ $image = wp_get_attachment_image_src( get_post_thumbnail_id( $post->ID ), 'post-thumbnail' ) ) &&
         $image[1] >= HEADER_IMAGE_WIDTH ) :
      // Houston, we have a new header image!
      echo get_the_post_thumbnail( $post->ID, 'post-thumbnail' );
   else : ?>
      <img src="<?php header_image(); ?>" width="<?php echo HEADER_IMAGE_WIDTH; ?>" height="<?php echo HEADER_IMAGE_HEIGHT; ?>" alt="" />
   <?php endif; ?>

Replace the else with an elseif which checks to see if the header image string is empty:

   elseif ( get_header_image() != "") : ?>