diff --git a/doc/misc/tramp.texi b/doc/misc/tramp.texi
index 5afc41b3a4b..ce409e23651 100644
--- a/doc/misc/tramp.texi
+++ b/doc/misc/tramp.texi
@@ -3937,6 +3937,9 @@ parallel.  In the following, on both remote hosts @samp{host1} and
 @trampfn{ssh@value{postfixhop}user2@@host2|docker,name,}
 @end example
 
+If you use the shortened name @samp{@trampfn{docker,name,}}, the last
+used proxy definition is expanded for.
+
 
 @node Home directories
 @section Expanding @file{~} to home directory
diff --git a/lisp/net/tramp-adb.el b/lisp/net/tramp-adb.el
index 83d9ebb6c63..4210d1247a8 100644
--- a/lisp/net/tramp-adb.el
+++ b/lisp/net/tramp-adb.el
@@ -811,10 +811,10 @@ will be used."
 	   v 'file-error "Cannot apply multibyte command `%s'" command))
 
 	(with-tramp-saved-connection-properties
-	    v '("process-name" "process-buffer")
+	    v '(" process-name" " process-buffer")
 	  ;; Set the new process properties.
-	  (tramp-set-connection-property v "process-name" name)
-	  (tramp-set-connection-property v "process-buffer" buffer)
+	  (tramp-set-connection-property v " process-name" name)
+	  (tramp-set-connection-property v " process-buffer" buffer)
 	  (with-current-buffer (tramp-get-connection-buffer v)
 	    (unwind-protect
 		;; We catch this event.  Otherwise, `make-process'
@@ -857,8 +857,8 @@ will be used."
 			;; We must flush them here already;
 			;; otherwise `rename-file', `delete-file'
 			;; or `insert-file-contents' will fail.
-			(tramp-flush-connection-property v "process-name")
-			(tramp-flush-connection-property v "process-buffer")
+			(tramp-flush-connection-property v " process-name")
+			(tramp-flush-connection-property v " process-buffer")
 			;; Copy tmpstderr file.
 			(when (and (stringp stderr)
 				   (not (tramp-tramp-file-p stderr)))
diff --git a/lisp/net/tramp-androidsu.el b/lisp/net/tramp-androidsu.el
index 1ee3cf296a1..9b45b416ff9 100644
--- a/lisp/net/tramp-androidsu.el
+++ b/lisp/net/tramp-androidsu.el
@@ -111,7 +111,7 @@ multibyte mode and waits for the shell prompt to appear."
 
   (with-tramp-debug-message vec "Opening connection"
     (let ((p (tramp-get-connection-process vec))
-	  (process-name (tramp-get-connection-property vec "process-name"))
+	  (process-name (tramp-get-connection-property vec " process-name"))
 	  (process-environment (copy-sequence process-environment)))
       ;; Open a new connection.
       (condition-case err
diff --git a/lisp/net/tramp-cache.el b/lisp/net/tramp-cache.el
index aa953c70582..9cbd20c21cb 100644
--- a/lisp/net/tramp-cache.el
+++ b/lisp/net/tramp-cache.el
@@ -68,7 +68,7 @@
 
 ;; Some properties are handled special:
 ;;
-;; - "process-name", "process-buffer" and "first-password-request" are
+;; - Properties which start with a space, like " process-name", are
 ;;   not saved in the file `tramp-persistency-file-name', although
 ;;   being connection properties related to a `tramp-file-name'
 ;;   structure.
@@ -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 " process-buffer")
 	    key))
      (hash-table-keys tramp-cache-data))))
 
@@ -586,10 +586,9 @@ PROPERTIES is a list of file properties (strings)."
 		    (not (tramp-file-name-localname key))
 		    (not (gethash "login-as" value))
 		    (not (gethash "started" value)))
-	       (progn
-		 (remhash "process-name" value)
-		 (remhash "process-buffer" value)
-		 (remhash "first-password-request" value))
+	       (dolist (k (hash-table-keys value))
+		 (when (string-prefix-p " " k)
+		   (remhash k value)))
 	     (remhash key cache)))
 	 cache)
 	;; Dump it.
diff --git a/lisp/net/tramp-cmds.el b/lisp/net/tramp-cmds.el
index f2ecf8173be..3a66030c9d0 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 " process-buffer")))
       (when (bufferp buf) (kill-buffer buf)))
 
     ;; Flush file cache.
diff --git a/lisp/net/tramp-crypt.el b/lisp/net/tramp-crypt.el
index 9b9c1986929..059b49714ab 100644
--- a/lisp/net/tramp-crypt.el
+++ b/lisp/net/tramp-crypt.el
@@ -352,7 +352,7 @@ connection if a previous connection has died for some reason."
 			   (tramp-compat-make-temp-file " .nocrypt" 'dir-flag))))
 	    ;; Enable `auth-source', unless "emacs -Q" has been called.
 	    (tramp-set-connection-property
-	     vec "first-password-request" tramp-cache-read-persistent-data)
+	     vec " first-password-request" tramp-cache-read-persistent-data)
 	    (with-temp-buffer
 	      (insert
 	       (tramp-read-passwd
@@ -408,7 +408,7 @@ ARGS are the arguments.  It returns t if ran successful, and nil otherwise."
 	   (args (delq nil args)))
       ;; Enable `auth-source', unless "emacs -Q" has been called.
       (tramp-set-connection-property
-       vec "first-password-request" tramp-cache-read-persistent-data)
+       vec " first-password-request" tramp-cache-read-persistent-data)
       (insert
        (tramp-read-passwd
 	(tramp-get-connection-process vec)
diff --git a/lisp/net/tramp-gvfs.el b/lisp/net/tramp-gvfs.el
index ed002d0d468..683f8cc12bd 100644
--- a/lisp/net/tramp-gvfs.el
+++ b/lisp/net/tramp-gvfs.el
@@ -1801,7 +1801,7 @@ a downcased host name only."
 	    (setq domain (read-string "Domain name: ")))
 
 	  (tramp-message l 6 "%S %S %S %d" message user domain flags)
-	  (unless (tramp-get-connection-property l "first-password-request")
+	  (unless (tramp-get-connection-property l " first-password-request")
 	    (tramp-clear-passwd l))
 
 	  (setq password (tramp-read-passwd
@@ -2252,7 +2252,7 @@ connection if a previous connection has died for some reason."
 
 	  ;; Enable `auth-source'.
 	  (tramp-set-connection-property
-	   vec "first-password-request" tramp-cache-read-persistent-data)
+	   vec " first-password-request" tramp-cache-read-persistent-data)
 
 	  ;; There will be a callback of "askPassword" when a password is needed.
 	  (dbus-register-method
diff --git a/lisp/net/tramp-sh.el b/lisp/net/tramp-sh.el
index 88d507ed75a..8f66b9f030e 100644
--- a/lisp/net/tramp-sh.el
+++ b/lisp/net/tramp-sh.el
@@ -2558,16 +2558,16 @@ The method used must be an out-of-band method."
       (with-temp-buffer
 	(unwind-protect
 	    (with-tramp-saved-connection-properties
-		v '("process-name" "process-buffer")
+		v '(" process-name" " process-buffer")
 	      ;; The default directory must be remote.
 	      (let ((default-directory
 		     (file-name-directory (if v1 filename newname)))
 		    (process-environment (copy-sequence process-environment)))
 		;; Set the transfer process properties.
 		(tramp-set-connection-property
-		 v "process-name" (buffer-name (current-buffer)))
+		 v " process-name" (buffer-name (current-buffer)))
 		(tramp-set-connection-property
-		 v "process-buffer" (current-buffer))
+		 v " process-buffer" (current-buffer))
 		(when copy-env
 		  (tramp-message
 		   v 6 "%s=\"%s\""
@@ -3075,10 +3075,10 @@ will be used."
 	   :file-handler t))
 
 	(with-tramp-saved-connection-properties
-	    v '("process-name"  "process-buffer")
+	    v '(" process-name"  " process-buffer")
 	  ;; Set the new process properties.
-	  (tramp-set-connection-property v "process-name" name)
-	  (tramp-set-connection-property v "process-buffer" buffer)
+	  (tramp-set-connection-property v " process-name" name)
+	  (tramp-set-connection-property v " process-buffer" buffer)
 	  (with-current-buffer (tramp-get-connection-buffer v)
 	    (unwind-protect
 		;; We catch this event.  Otherwise, `make-process'
@@ -3160,8 +3160,8 @@ will be used."
 			(set-marker (process-mark p) (point)))
 		      ;; We must flush them here already; otherwise
 		      ;; `delete-file' will fail.
-		      (tramp-flush-connection-property v "process-name")
-		      (tramp-flush-connection-property v "process-buffer")
+		      (tramp-flush-connection-property v " process-name")
+		      (tramp-flush-connection-property v " process-buffer")
 		      ;; Kill stderr process and delete named pipe.
 		      (when (bufferp stderr)
 			(add-function
@@ -4319,7 +4319,7 @@ file exists and nonzero exit status otherwise."
 (defun tramp-find-shell (vec)
   "Open a shell on the remote host which groks tilde expansion."
   ;; If we are in `make-process', we don't need another shell.
-  (unless (tramp-get-connection-property vec "process-name")
+  (unless (tramp-get-connection-property vec " process-name")
     (with-current-buffer (tramp-get-buffer vec)
       (let ((default-shell (tramp-get-method-parameter vec 'tramp-remote-shell))
 	    shell)
@@ -4424,7 +4424,7 @@ process to set up.  VEC specifies the connection."
   (let* ((old-uname (tramp-get-connection-property vec "uname"))
 	 (uname
 	  ;; If we are in `make-process', we don't need to recompute.
-	  (if (and old-uname (tramp-get-connection-property vec "process-name"))
+	  (if (and old-uname (tramp-get-connection-property vec " process-name"))
 	      old-uname
 	    (tramp-set-connection-property
 	     vec "uname"
@@ -4438,7 +4438,7 @@ process to set up.  VEC specifies the connection."
 	  (and config-check-function
 	       ;; If we are in `make-process', we don't need to recompute.
 	       (if (and old-config-check
-			(tramp-get-connection-property vec "process-name"))
+			(tramp-get-connection-property vec " process-name"))
 		   old-config-check
 		 (tramp-set-connection-property
 		  vec "config-check-data"
@@ -5106,7 +5106,7 @@ connection if a previous connection has died for some reason."
 
   (with-tramp-debug-message vec "Opening connection"
     (let ((p (tramp-get-connection-process vec))
-	  (process-name (tramp-get-connection-property vec "process-name"))
+	  (process-name (tramp-get-connection-property vec " process-name"))
 	  (process-environment (copy-sequence process-environment))
 	  (pos (with-current-buffer (tramp-get-connection-buffer vec) (point))))
 
diff --git a/lisp/net/tramp-smb.el b/lisp/net/tramp-smb.el
index f4d05de40f5..797e481e3fb 100644
--- a/lisp/net/tramp-smb.el
+++ b/lisp/net/tramp-smb.el
@@ -526,13 +526,13 @@ arguments to pass to the OPERATION."
 
 		  (unwind-protect
 		      (with-tramp-saved-connection-properties
-			  v '("process-name" "process-buffer")
+			  v '(" process-name" " process-buffer")
 			(with-temp-buffer
 			  ;; Set the transfer process properties.
 			  (tramp-set-connection-property
-			   v "process-name" (buffer-name (current-buffer)))
+			   v " process-name" (buffer-name (current-buffer)))
 			  (tramp-set-connection-property
-			   v "process-buffer" (current-buffer))
+			   v " process-buffer" (current-buffer))
 
 			  (when t1
 			    ;; The smbclient tar command creates
@@ -799,13 +799,13 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
 				(concat "2>" (tramp-get-remote-null-device v)))))
 
 	    (with-tramp-saved-connection-properties
-		v '("process-name" "process-buffer")
+		v '(" process-name" " process-buffer")
 	      (with-temp-buffer
 		;; Set the transfer process properties.
 		(tramp-set-connection-property
-		 v "process-name" (buffer-name (current-buffer)))
+		 v " process-name" (buffer-name (current-buffer)))
 		(tramp-set-connection-property
-		 v "process-buffer" (current-buffer))
+		 v " process-buffer" (current-buffer))
 
 		;; Use an asynchronous process.  By this, password
 		;; can be handled.
@@ -1247,11 +1247,11 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
       ;; Call it.
       (condition-case nil
 	  (with-tramp-saved-connection-properties
-	      v '("process-name" "process-buffer")
+	      v '(" process-name" " process-buffer")
 	    ;; Set the new process properties.
-	    (tramp-set-connection-property v "process-name" name1)
+	    (tramp-set-connection-property v " process-name" name1)
 	    (tramp-set-connection-property
-	     v "process-buffer"
+	     v " process-buffer"
 	     (or outbuf (generate-new-buffer tramp-temp-buffer-name)))
 	    (with-current-buffer (tramp-get-connection-buffer v)
 	      ;; Preserve buffer contents.
@@ -1287,9 +1287,9 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
       ;; Cleanup.  We remove all file cache values for the connection,
       ;; because the remote process could have changed them.
       (when tmpinput (delete-file tmpinput))
-      ;; FIXME: Does connection-property "process-buffer" still exist?
+      ;; FIXME: Does connection-property " process-buffer" still exist?
       (unless outbuf
-	(kill-buffer (tramp-get-connection-property v "process-buffer")))
+	(kill-buffer (tramp-get-connection-property v " process-buffer")))
       (when process-file-side-effects
 	(tramp-flush-directory-properties v "/"))
 
@@ -1388,13 +1388,13 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
 			      "||" "echo" "tramp_exit_status" "1")))
 
 	  (with-tramp-saved-connection-properties
-	      v '("process-name" "process-buffer")
+	      v '(" process-name" " process-buffer")
 	    (with-temp-buffer
 	      ;; Set the transfer process properties.
 	      (tramp-set-connection-property
-	       v "process-name" (buffer-name (current-buffer)))
+	       v " process-name" (buffer-name (current-buffer)))
 	      (tramp-set-connection-property
-	       v "process-buffer" (current-buffer))
+	       v " process-buffer" (current-buffer))
 
 	      ;; Use an asynchronous process.  By this, password
 	      ;; can be handled.
@@ -1450,7 +1450,7 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
 	   p)
       (unwind-protect
 	  (with-tramp-saved-connection-properties
-	      v '("process-name" "process-buffer")
+	      v '(" process-name" " process-buffer")
 	    (save-excursion
 	      (save-restriction
 		(while (get-process name1)
@@ -1458,8 +1458,8 @@ PRESERVE-UID-GID and PRESERVE-EXTENDED-ATTRIBUTES are completely ignored."
 		  (setq i (1+ i)
 			name1 (format "%s<%d>" name i)))
 		;; Set the new process properties.
-		(tramp-set-connection-property v "process-name" name1)
-		(tramp-set-connection-property v "process-buffer" buffer)
+		(tramp-set-connection-property v " process-name" name1)
+		(tramp-set-connection-property v " process-buffer" buffer)
 		;; Activate narrowing in order to save BUFFER contents.
 		(with-current-buffer (tramp-get-connection-buffer v)
 		  (let ((buffer-undo-list t))
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index 0a61ca7e40d..dbec3d5807e 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -1956,11 +1956,11 @@ 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"
+	  ;; We use the existence of connection property " process-buffer"
 	  ;; as indication, whether a connection is active.
 	  (tramp-set-connection-property
-	   vec "process-buffer"
-	   (tramp-get-connection-property vec "process-buffer"))
+	   vec " process-buffer"
+	   (tramp-get-connection-property vec " process-buffer"))
 	  (setq buffer-undo-list t
 		default-directory
 		(tramp-make-tramp-file-name vec 'noloc))
@@ -1972,14 +1972,14 @@ Unless DONT-CREATE, the buffer is created when it doesn't exist yet."
 Unless DONT-CREATE, the buffer is created when it doesn't exist yet.
 In case a second asynchronous communication has been started, it is different
 from `tramp-get-buffer'."
-  (or (tramp-get-connection-property vec "process-buffer")
+  (or (tramp-get-connection-property vec " process-buffer")
       (tramp-get-buffer vec dont-create)))
 
 (defun tramp-get-connection-name (vec)
   "Get the connection name to be used for VEC.
 In case a second asynchronous communication has been started, it is different
 from the default one."
-  (or (tramp-get-connection-property vec "process-name")
+  (or (tramp-get-connection-property vec " process-name")
       (tramp-buffer-name vec)))
 
 (defun tramp-get-unique-process-name (name)
@@ -2477,7 +2477,7 @@ Fall back to normal file name handler if no Tramp file name handler exists."
 			(with-tramp-debug-message
 			    v (format "Running `%S'" (cons operation args))
 			  ;; We flush connection properties
-			  ;; "process-name" and "process-buffer",
+			  ;; " process-name" and " process-buffer",
 			  ;; because the operations shall be applied
 			  ;; in the main connection process.  In order
 			  ;; to avoid superfluous debug buffers during
@@ -2492,12 +2492,12 @@ Fall back to normal file name handler if no Tramp file name handler exists."
 		          ;; a short time frame.
 		          ;; In both cases, we try the default handler then.
 			  (with-tramp-saved-connection-properties
-			      v '("process-name" "process-buffer")
+			      v '(" process-name" " process-buffer")
 			    (let ((tramp-verbose
 				   (if minibuffer-completing-file-name
 				       0 tramp-verbose)))
-			      (tramp-flush-connection-property v "process-name")
-			      (tramp-flush-connection-property v "process-buffer"))
+			      (tramp-flush-connection-property v " process-name")
+			      (tramp-flush-connection-property v " process-buffer"))
 		            (setq result
 				  (catch 'non-essential
 			            (catch 'suppress
@@ -5694,7 +5694,7 @@ of."
       ;; Sometimes, the process returns a new password request
       ;; immediately after rejecting the previous (wrong) one.
       (unless (or tramp-password-prompt-not-unique
-		  (tramp-get-connection-property vec "first-password-request"))
+		  (tramp-get-connection-property vec " first-password-request"))
 	(tramp-clear-passwd vec))
       (goto-char (point-min))
       (tramp-check-for-regexp proc tramp-process-action-regexp)
@@ -5901,7 +5901,7 @@ performed successfully.  Any other value means an error."
   (tramp-set-connection-property
    (tramp-get-connection-property
     proc "password-vector" (process-get proc 'tramp-vector))
-   "first-password-request" tramp-cache-read-persistent-data)
+   " first-password-request" tramp-cache-read-persistent-data)
   (save-restriction
     (with-tramp-progress-reporter
 	proc 3 "Waiting for prompts from remote shell"
@@ -6872,7 +6872,8 @@ Consults the auth-source package."
 	 (setq tramp-password-save-function nil)
 	 ;; See if auth-sources contains something useful.
 	 (ignore-errors
-	   (and (tramp-get-connection-property vec "first-password-request")
+	   (and auth-sources
+                (tramp-get-connection-property vec " first-password-request")
 		;; Try with Tramp's current method.  If there is no
 		;; user name, `:create' triggers to ask for.  We
 		;; suppress it.
@@ -6894,7 +6895,7 @@ Consults the auth-source package."
 		 (lambda () (password-cache-add key auth-passwd)))
 	   auth-passwd))
 
-      (tramp-set-connection-property vec "first-password-request" nil))))
+      (tramp-set-connection-property vec " first-password-request" nil))))
 
 (defun tramp-read-passwd-without-cache (proc &optional prompt)
   "Read a password from user (compat function)."