--- message.el.orig	Sat Nov  6 04:15:15 1999
+++ message.el	Thu Nov 11 02:25:28 1999
@@ -2939,14 +2939,15 @@
   (let ((system-name (system-name))
 	(user-mail (message-user-mail-address)))
     (cond
-     ((string-match "[^.]\\.[^.]" system-name)
-      ;; `system-name' returned the right result.
-      system-name)
      ;; Try `mail-host-address'.
      ((and (boundp 'mail-host-address)
 	   (stringp mail-host-address)
 	   (string-match "\\." mail-host-address))
       mail-host-address)
+     ;; Else try `system-name'
+     ((string-match "[^.]\\.[^.]" system-name)
+      ;; `system-name' returned the right result.
+      system-name)
      ;; We try `user-mail-address' as a backup.
      ((and user-mail
 	   (string-match "\\." user-mail)