Index: wp-includes/class-phpmailer.php
===================================================================
--- wp-includes/class-phpmailer.php	(revision 29296)
+++ wp-includes/class-phpmailer.php	(working copy)
@@ -410,7 +410,7 @@
      *   string  $subject       the subject
      *   string  $body          the email body
      *   string  $from          email address of sender
-     * 
+     *
      * @type string
      */
     public $action_function = '';
@@ -1667,6 +1667,7 @@
     public function getMailMIME()
     {
         $result = '';
+        $ismultipart = true;
         switch ($this->message_type) {
             case 'inline':
                 $result .= $this->headerLine('Content-Type', 'multipart/related;');
@@ -1687,11 +1688,20 @@
             default:
                 // Catches case 'plain': and case '':
                 $result .= $this->textLine('Content-Type: ' . $this->ContentType . '; charset=' . $this->CharSet);
+                $ismultipart = false;
                 break;
         }
         //RFC1341 part 5 says 7bit is assumed if not specified
         if ($this->Encoding != '7bit') {
-            $result .= $this->headerLine('Content-Transfer-Encoding', $this->Encoding);
+            //RFC 2045 section 6.4 says multipart MIME parts may only use 7bit, 8bit or binary CTE
+            if ($ismultipart) {
+                if ($this->Encoding == '8bit') {
+                    $result .= $this->headerLine('Content-Transfer-Encoding', '8bit');
+                }
+                //The only remaining alternatives are quoted-printable and base64, which are both 7bit compatible
+            } else {
+                $result .= $this->headerLine('Content-Transfer-Encoding', $this->Encoding);
+            }
         }
 
         if ($this->Mailer != 'mail') {