OK, I solved this, with some code from Hedengren’s Smashing WordPress Themes.
Give your child theme a functions.php file. Paste in the following code. Don’t leave any white space or blank lines after the code, btw. This defines your header image as 940×130. Hack and style as needed.
<?php
define('HEADER_TEXTCOLOR', 'ffffff');
define('HEADER_IMAGE', get_bloginfo('stylesheet_directory') . '/images/header-default.jpg');
define('HEADER_IMAGE_WIDTH', 940);
define('HEADER_IMAGE_HEIGHT', 130);
// The site header function
function site_header_style() {
?><style type="text/css">
div#header {
background: url(<?php header_image(); ?>);
}
</style><?php
}
// The admin header function
function admin_header_style() {
?><style type="text/css">
#headimg {
width: <?php echo HEADER_IMAGE_WIDTH; ?>px;
height: <?php echo HEADER_IMAGE_HEIGHT; ?>px;
}
</style><?php
}
// Enable!
add_custom_image_header('site_header_style', 'admin_header_style');
?>