Index: wp-includes/comment-template.php
===================================================================
--- wp-includes/comment-template.php	(revision 16706)
+++ wp-includes/comment-template.php	(working copy)
@@ -1533,7 +1533,7 @@
 		'comment_field'        => '<p class="comment-form-comment"><label for="comment">' . _x( 'Comment', 'noun' ) . '</label><textarea id="comment" name="comment" cols="45" rows="8" aria-required="true"></textarea></p>',
 		'must_log_in'          => '<p class="must-log-in">' .  sprintf( __( 'You must be <a href="%s">logged in</a> to post a comment.' ), wp_login_url( apply_filters( 'the_permalink', get_permalink( $post_id ) ) ) ) . '</p>',
 		'logged_in_as'         => '<p class="logged-in-as">' . sprintf( __( 'Logged in as <a href="%1$s">%2$s</a>. <a href="%3$s" title="Log out of this account">Log out?</a>' ), admin_url( 'profile.php' ), $user_identity, wp_logout_url( apply_filters( 'the_permalink', get_permalink( $post_id ) ) ) ) . '</p>',
-		'comment_notes_before' => '<p class="comment-notes">' . __( 'Your email address will not be published.' ) . ( $req ? $required_text : '' ) . '</p>',
+		'comment_notes_before' => is_user_logged_in() ? '' : '<p class="comment-notes">' . __( 'Your email address will not be published.' ) . ( $req ? $required_text : '' ) . '</p>',
 		'comment_notes_after'  => '<p class="form-allowed-tags">' . sprintf( __( 'You may use these <abbr title="HyperText Markup Language">HTML</abbr> tags and attributes: %s' ), ' <code>' . allowed_tags() . '</code>' ) . '</p>',
 		'id_form'              => 'commentform',
 		'id_submit'            => 'submit',
@@ -1556,11 +1556,11 @@
 				<?php else : ?>
 					<form action="<?php echo site_url( '/wp-comments-post.php' ); ?>" method="post" id="<?php echo esc_attr( $args['id_form'] ); ?>">
 						<?php do_action( 'comment_form_top' ); ?>
+						<?php echo $args['comment_notes_before']; ?>
 						<?php if ( is_user_logged_in() ) : ?>
 							<?php echo apply_filters( 'comment_form_logged_in', $args['logged_in_as'], $commenter, $user_identity ); ?>
 							<?php do_action( 'comment_form_logged_in_after', $commenter, $user_identity ); ?>
 						<?php else : ?>
-							<?php echo $args['comment_notes_before']; ?>
 							<?php
 							do_action( 'comment_form_before_fields' );
 							foreach ( (array) $args['fields'] as $name => $field ) {