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Index: domain_mapping.php
===================================================================
--- domain_mapping.php (revision 688919)
+++ domain_mapping.php	(working copy)
@@ -685,7 +685,7 @@
 }
 
 function redirect_to_mapped_domain() {
-	global $current_blog, $wpdb;
+	global $current_blog, $wpdb, $wp_customize;
 
 	// don't redirect the main site
 	if ( is_main_site() )
@@ -695,7 +695,7 @@
 		return;
 
 	// don't redirect theme customizer (WP 3.4)
-	if ( isset( $_POST['customize'] ) && isset( $_POST['theme'] ) && $_POST['customize'] == 'on' )
+	if ( is_a( $wp_customize, 'WP_Customize_Manager' ) )
 		return;
 
 	$protocol = is_ssl() ? 'https://' : 'http://';