To remove WordPress 3.3 admin bar but left user and front end links intact (so restore the header to the 3.2 version) without plugin, you should put this into your functions.php or custom plugin:
function remove_admin_bar_links() {
global $wp_admin_bar;
$wp_admin_bar->remove_menu('wp-logo');
$wp_admin_bar->remove_menu('view-site');
$wp_admin_bar->remove_menu('new-content');
$wp_admin_bar->remove_menu('comments');
}
add_action( 'wp_before_admin_bar_render', 'remove_admin_bar_links' );
and add stylesheet with these lines to your admin_head:
#wpadminbar {left:146px;background-color:#fff; background-image:none;z-index:9;border-bottom: 1px solid #ccc;
-moz-box-shadow: 0px 2px 2px rgba(50, 50, 50, .1);
-webkit-box-shadow: 0px 2px 2px rgba(50, 50, 50, .1);
-box-shadow: 0px 2px 2px rgba(50, 50, 50, .1);}
#wpadminbar .ab-top-secondary {margin-right:146px;background-color:#fff; background-image:none;}
.folded #wpadminbar .ab-top-secondary {margin-right:32px;}
body.admin-bar #adminmenu {padding-top:0px;}
#wpadminbar * {text-shadow: none; color: #444;}
#wpadminbar .ab-top-menu > li:hover > .ab-item, #wpadminbar .ab-top-menu > li.hover > .ab-item, #wpadminbar .ab-top-menu > li > .ab-item:focus, #wpadminbar.nojq .quicklinks .ab-top-menu > li > .ab-item:focus {background-color:#fff; background-image:none; color: #444; text-decoration: underline;}
#wpadminbar .quicklinks .ab-top-secondary > li, #wpadminbar .quicklinks .ab-top-secondary > li a {border:0;}
#wpadminbar .menupop .ab-sub-wrapper, #wpadminbar .shortlink-input {
-moz-box-shadow: -2px 2px 2px rgba(50, 50, 50, .1);
-webkit-box-shadow: -2px 2px 2px rgba(50, 50, 50, .1);
-box-shadow: -2px 2px 2px rgba(50, 50, 50, .1);
border-color: #ccc;}
#wpadminbar .quicklinks a {padding: 0 15px;}
Works like a charm for me.