Index: wp-includes/class-phpmailer.php
===================================================================
--- wp-includes/class-phpmailer.php	(revision 19632)
+++ wp-includes/class-phpmailer.php	(working copy)
@@ -1190,11 +1190,15 @@
     } else {
       $result .= sprintf("Message-ID: <%s@%s>%s", $uniq_id, $this->ServerHostname(), $this->LE);
     }
-    $result .= $this->HeaderLine('X-Priority', $this->Priority);
-    if($this->XMailer) {
-      $result .= $this->HeaderLine('X-Mailer', $this->XMailer);
-    } else {
-      $result .= $this->HeaderLine('X-Mailer', 'PHPMailer '.$this->Version.' (http://code.google.com/a/apache-extras.org/p/phpmailer/)');
+    // To disable sending these optional X- headers set the values to false
+    if ( false !== $this->Priority )
+        $result .= $this->HeaderLine('X-Priority', $this->Priority);
+    if ( false !== $this->XMailer ) {
+        if($this->XMailer) {
+          $result .= $this->HeaderLine('X-Mailer', $this->XMailer);
+        } else {
+          $result .= $this->HeaderLine('X-Mailer', 'PHPMailer '.$this->Version.' (http://code.google.com/a/apache-extras.org/p/phpmailer/)');
+        }
     }
 
     if($this->ConfirmReadingTo != '') {