functions.php for twentyten child theme

<?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');

remove_action( 'widgets_init', 'twentyten_widgets_init' ); //necessary to replace parent theme's code
    function twentyten_child_widgets_init() {
        register_sidebar( array(
        'name' => __( 'Alt Primary Widget Area', 'twentyten' ),
        'id' => 'alt-primary-widget-area',
        'description' => __( 'Alt primary widget area', 'twentyten' ),
        'before_widget' => '<li id="%1$s" class="widget-container %2$s">',
        'after_widget' => '</li>',
        'before_title' => '<h3 class="widget-title">',
        'after_title' => '</h3>',
    ) );
}
/** Register sidebars by running twentyten_widgets_init() on the widgets_init hook. */
add_action( 'widgets_init', 'twentyten_child_widgets_init' );
?>