After some trial and error, this is what it took to make it work…
$cat_args = array('orderby' => 'count');
$cat_args['title_li'] = '';
$cat_args['exclude_tree'] = 1;
$cat_args['exclude'] = 1;
$cat_args['depth'] = 1;
wp_list_categories(apply_filters('widget_categories_args', $cat_args));