diff --git a/lisp/net/tramp-integration.el b/lisp/net/tramp-integration.el
index 552d52835e9..6df9b17cdc3 100644
--- a/lisp/net/tramp-integration.el
+++ b/lisp/net/tramp-integration.el
@@ -59,8 +59,9 @@
 
 ;;; Fontification of `read-file-name':
 
-(defvar tramp-rfn-eshadow-overlay)
-(make-variable-buffer-local 'tramp-rfn-eshadow-overlay)
+;; An overlay covering the shadowed part of the filename (local to the
+;; minibuffer).
+(defvar-local tramp-rfn-eshadow-overlay nil)
 
 (defun tramp-rfn-eshadow-setup-minibuffer ()
   "Set up a minibuffer for `file-name-shadow-mode'.
@@ -104,7 +105,8 @@ been set up by `rfn-eshadow-setup-minibuffer'."
 		   (minibuffer-prompt-end)))
 	  ;; We do not want to send any remote command.
 	  (non-essential t))
-      (when (tramp-tramp-file-p (buffer-substring end (point-max)))
+      (when (and (tramp-tramp-file-p (buffer-substring end (point-max)))
+		 (not (file-name-quoted-p (buffer-substring end (point-max)))))
 	(save-excursion
 	  (save-restriction
 	    (narrow-to-region
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index 6c1a4ae7127..e0e080021c7 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -4076,6 +4076,7 @@ Let-bind it when necessary.")
   ;; Otherwise, remove any trailing slash from localname component.
   ;; Method, host, etc, are unchanged.
   (while (with-parsed-tramp-file-name directory nil
+	   (setq localname (file-name-unquote localname))
 	   (and (tramp-compat-length> localname 0)
 		(eq (aref localname (1- (length localname))) ?/)
 		(not (string= localname "/"))))
@@ -4164,8 +4165,8 @@ Let-bind it when necessary.")
     (eq (file-attribute-type (file-attributes (file-truename filename))) t)))
 
 (defun tramp-handle-file-equal-p (filename1 filename2)
-  "Like `file-equalp-p' for Tramp files."
-  ;; Native `file-equalp-p' calls `file-truename', which requires a
+  "Like `file-equal-p' for Tramp files."
+  ;; Native `file-equal-p' calls `file-truename', which requires a
   ;; remote connection.  This can be avoided, if FILENAME1 and
   ;; FILENAME2 are not located on the same remote host.
   (when (tramp-equal-remote