Index: comment.module
===================================================================
RCS file: /cvs/drupal/drupal/modules/comment/comment.module,v
retrieving revision 1.822
diff -u -r1.822 comment.module
--- comment.module	26 Dec 2009 16:50:08 -0000	1.822
+++ comment.module	31 Dec 2009 09:28:41 -0000
@@ -292,6 +292,9 @@
     'post comments without approval' => array(
       'title' => t('Post comments without approval'),
     ),
+    'edit own comments' => array(
+      'title' => t('Edit own comments'),
+    ),
   );
 }
 
@@ -1256,7 +1259,7 @@
   global $user;
 
   if ($op == 'edit') {
-    return ($user->uid && $user->uid == $comment->uid && comment_num_replies($comment->cid) == 0) || user_access('administer comments');
+    return ($user->uid && $user->uid == $comment->uid && user_access('edit own comments')) || user_access('administer comments');
   }
 }
 
Index: comment.test
===================================================================
RCS file: /cvs/drupal/drupal/modules/comment/comment.test,v
retrieving revision 1.59
diff -u -r1.59 comment.test
--- comment.test	16 Dec 2009 19:53:53 -0000	1.59
+++ comment.test	31 Dec 2009 09:28:42 -0000
@@ -10,7 +10,7 @@
     parent::setUp('comment', 'search');
     // Create users and test node.
     $this->admin_user = $this->drupalCreateUser(array('administer content types', 'administer comments', 'administer blocks'));
-    $this->web_user = $this->drupalCreateUser(array('access comments', 'post comments', 'create article content'));
+    $this->web_user = $this->drupalCreateUser(array('access comments', 'post comments', 'create article content', 'edit own comments'));
     $this->node = $this->drupalCreateNode(array('type' => 'article', 'promote' => 1, 'uid' => $this->web_user->uid));
   }