Add credit to get_custom_header in alt

Use this for the alt="" attribute on the custom header <img> tag …

alt="<?php  
$attachment_id = get_custom_header()->attachment_id;
$alt = get_post_meta( $attachment_id, '_wp_attachment_image_alt', true );
if ( count( $alt ) ) echo $alt;
?>" />

… and then just edit the media attachment and add the alt text.