diff --git a/lisp/net/tramp-cache.el b/lisp/net/tramp-cache.el
index 95fff9db0b4..d432deee5d1 100644
--- a/lisp/net/tramp-cache.el
+++ b/lisp/net/tramp-cache.el
@@ -554,7 +554,7 @@ PROPERTIES is a list of file properties (strings)."
      (lambda (key)
        (and (tramp-file-name-p key)
 	    (null (tramp-file-name-localname key))
-	    (tramp-connection-property-p key " process-buffer")
+	    (tramp-connection-property-p key " connected")
 	    key))
      (hash-table-keys tramp-cache-data))))
 
diff --git a/lisp/net/tramp-cmds.el b/lisp/net/tramp-cmds.el
index a469df1b872..71829e81093 100644
--- a/lisp/net/tramp-cmds.el
+++ b/lisp/net/tramp-cmds.el
@@ -173,7 +173,7 @@ interactively, a Tramp connection has to be selected."
 		     (get-buffer (tramp-debug-buffer-name vec)))
 		   (unless keep-debug
 		     (get-buffer (tramp-trace-buffer-name vec)))
-		   (tramp-get-connection-property vec " process-buffer")))
+		   (tramp-get-connection-property vec " connected")))
       (when (bufferp buf) (kill-buffer buf)))
 
     ;; Flush file cache.
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index 1241d321b9b..d87cecb9ec6 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -2002,10 +2002,11 @@ Unless DONT-CREATE, the buffer is created when it doesn't exist yet."
   (or (get-buffer (tramp-buffer-name vec))
       (unless dont-create
 	(with-current-buffer (get-buffer-create (tramp-buffer-name vec))
-	  ;; We use the existence of connection property " process-buffer"
-	  ;; as indication, whether a connection is active.
+	  ;; We use the existence of connection property " connected"
+	  ;; as indication, whether a connection is active.  It keeps
+	  ;; the connection buffer, for cleanup.
 	  (tramp-set-connection-property
-	   vec " process-buffer"
+	   vec " connected"
 	   (tramp-get-connection-property vec " process-buffer"))
 	  (setq buffer-undo-list t
 		default-directory