Index: wp-content/themes/twentythirteen/style.css
===================================================================
--- wp-content/themes/twentythirteen/style.css	(revision 23470)
+++ wp-content/themes/twentythirteen/style.css	(working copy)
@@ -2256,13 +2256,17 @@
 	margin-bottom: 10px;
 }
 
-.comment-author .fn,
+.comment-meta .fn,
 .comment-reply-link {
 	color: #ed331c;
 	font-size: 14px;
 	font-style: normal;
 }
 
+.comment-meta .fn a {
+	color: #f94a0a;
+}
+
 .bypostauthor .fn:before {
 	content: '\f408';
 }
@@ -2280,6 +2284,12 @@
 	width:         calc(100% - 124px);
 }
 
+.comment.no-avatar .comment-meta,
+.comment.no-avatar .comment-content,
+.comment.no-avatar .reply {
+	width: 100%;
+}
+
 .comment-meta,
 .comment-meta a {
 	color: #a2a2a2;
Index: wp-content/themes/twentythirteen/functions.php
===================================================================
--- wp-content/themes/twentythirteen/functions.php	(revision 23470)
+++ wp-content/themes/twentythirteen/functions.php	(working copy)
@@ -344,14 +344,16 @@
 	?>
 	<li id="li-comment-<?php comment_ID(); ?>">
 		<article id="comment-<?php comment_ID(); ?>" <?php comment_class(); ?>>
+			<?php if ( $avatar = get_avatar( $comment, 74 ) ) : ?>
 			<div class="comment-author vcard">
-				<?php echo get_avatar( $comment, 74 ); ?>
-				<cite class="fn"><?php comment_author_link(); ?></cite>
+				<?php echo $avatar; ?>
 			</div><!-- .comment-author -->
+			<?php endif; ?>
 
 			<header class="comment-meta">
 				<?php
-					printf( '<a href="%1$s"><time datetime="%2$s">%3$s</time></a>',
+					printf( '<cite class="fn">%1$s</cite> on <a href="%2$s"><time datetime="%3$s">%4$s</time></a>',
+						get_comment_author_link(),
 						esc_url( get_comment_link( $comment->comment_ID ) ),
 						get_comment_time( 'c' ),
 						sprintf( _x( '%1$s at %2$s', '1: date, 2: time', 'twentythirteen' ), get_comment_date(), get_comment_time() )
@@ -378,6 +380,23 @@
 }
 endif;
 
+/**
+ * Extends the default WordPress comment class to denote whether showing avatars
+ * is enabled.
+ *
+ * @since Twenty Thirteen 1.0
+ *
+ * @param array $classes Existing class values.
+ * @return array Filtered class values.
+ */
+function twentythirteen_comment_class( $classes ) {
+	if ( ! get_option( 'show_avatars' ) )
+		$classes[] = 'no-avatar';
+
+	return $classes;
+}
+add_filter( 'comment_class', 'twentythirteen_comment_class' );
+
 if ( ! function_exists( 'twentythirteen_entry_meta' ) ) :
 /**
  * Prints HTML with meta information for current post: categories, tags, permalink, author, and date.