Index: wp-admin/includes/dashboard.php
===================================================================
--- wp-admin/includes/dashboard.php	(revision 22085)
+++ wp-admin/includes/dashboard.php	(working copy)
@@ -1240,7 +1240,7 @@
 	<div class="welcome-panel-column">
 		<h4><?php _e( 'Get Started' ); ?></h4>
 		<p><?php _e( 'First, tweak the look of your site:' ); ?></p>
-		<a class="button-primary welcome-button" href="<?php echo add_query_arg( 'url', urlencode( admin_url( '/' ) ), wp_customize_url() ); ?>"><?php _e( 'Customize Your Site' ); ?></a>
+		<a class="button-primary welcome-button hide-if-no-customize" href="<?php echo add_query_arg( 'url', urlencode( admin_url( '/' ) ), wp_customize_url() ); ?>"><?php _e( 'Customize Your Site' ); ?></a>
 		<?php if ( current_user_can( 'install_themes' ) || ( current_user_can( 'switch_themes' ) && count( wp_get_themes( array( 'allowed' => true ) ) ) > 1 ) ) : ?>
 			<p><?php printf( __( 'or, <a href="%s">change your theme completely</a>' ), admin_url( 'themes.php' ) ); ?></p>
 		<?php endif; ?>
Index: wp-admin/admin-header.php
===================================================================
--- wp-admin/admin-header.php	(revision 22085)
+++ wp-admin/admin-header.php	(working copy)
@@ -105,7 +105,8 @@
 <?php
 // If the customize-loader script is enqueued, make sure the customize
 // body classes are correct as early as possible.
-if ( wp_script_is( 'customize-loader', 'queue' ) && current_user_can( 'edit_theme_options' ) )
+if ( ( wp_script_is( 'customize-loader', 'queue' ) || 'dashboard' == $current_screen->base )
+	&& current_user_can( 'edit_theme_options' ) )
 	wp_customize_support_script();
 ?>