Index: wp-includes/admin-bar.php
===================================================================
--- wp-includes/admin-bar.php	(revision 19546)
+++ wp-includes/admin-bar.php	(working copy)
@@ -125,6 +125,17 @@
 }
 
 /**
+ * Rebinds the "My Account" item to allow items to be placed before it.
+ *
+ * @since 3.3.0
+ */
+function wp_admin_bar_my_account_item( $wp_admin_bar ) {
+	$node = $wp_admin_bar->get_node( 'my-account' );
+	$wp_admin_bar->remove_node( 'my-account' );
+	$wp_admin_bar->add_node( $node );
+}
+
+/**
  * Add the "My Account" menu and all submenus.
  *
  * @since 3.1.0
Index: wp-includes/class-wp-admin-bar.php
===================================================================
--- wp-includes/class-wp-admin-bar.php	(revision 19546)
+++ wp-includes/class-wp-admin-bar.php	(working copy)
@@ -352,8 +352,9 @@
 
 	public function add_menus() {
 		// User related, aligned right.
-		add_action( 'admin_bar_menu', 'wp_admin_bar_search_menu', 10 );
-		add_action( 'admin_bar_menu', 'wp_admin_bar_my_account_menu', 20 );
+		add_action( 'admin_bar_menu', 'wp_admin_bar_my_account_menu', 0 );
+		add_action( 'admin_bar_menu', 'wp_admin_bar_search_menu', 4 );
+		add_action( 'admin_bar_menu', 'wp_admin_bar_my_account_item', 7 );
 
 		// Site related.
 		add_action( 'admin_bar_menu', 'wp_admin_bar_wp_menu', 10 );