diff --git a/doc/misc/tramp.texi b/doc/misc/tramp.texi
index 7b3a4808a45..7ddf6758ae5 100644
--- a/doc/misc/tramp.texi
+++ b/doc/misc/tramp.texi
@@ -678,7 +678,10 @@ not auto loaded by Emacs.  All examples require @value{tramp} to be
 installed and loaded:
 
 @lisp
+@group
+(require 'tramp)
 (customize-set-variable 'tramp-verbose 6 "Enable remote command traces")
+@end group
 @end lisp
 
 For functions used to configure @value{tramp}, the following clause
diff --git a/lisp/net/tramp-cache.el b/lisp/net/tramp-cache.el
index c8223d859c7..941c502fa83 100644
--- a/lisp/net/tramp-cache.el
+++ b/lisp/net/tramp-cache.el
@@ -253,19 +253,19 @@ Return VALUE."
 
 (defun tramp-flush-file-upper-properties (key file)
   "Remove some properties of FILE's upper directory."
-  (when (file-name-absolute-p file)
-    ;; `file-name-directory' can return nil, for example for "~".
-    (when-let* ((file (file-name-directory file))
-		(file (directory-file-name file)))
-      (setq key (tramp-file-name-unify key file))
-      (unless (eq key tramp-cache-undefined)
-	(dolist (property (hash-table-keys (tramp-get-hash-table key)))
-	  (when (string-match-p
-		 (rx
-		  bos (| "directory-" "file-name-all-completions"
-			 "file-entries"))
-		 property)
-	    (tramp-flush-file-property key file property)))))))
+  (when-let* (((file-name-absolute-p file))
+	      ;; `file-name-directory' can return nil, for example for "~".
+	      (file (file-name-directory file))
+	      (file (directory-file-name file)))
+    (setq key (tramp-file-name-unify key file))
+    (unless (eq key tramp-cache-undefined)
+      (dolist (property (hash-table-keys (tramp-get-hash-table key)))
+	(when (string-match-p
+	       (rx
+		bos (| "directory-" "file-name-all-completions"
+		       "file-entries"))
+	       property)
+	  (tramp-flush-file-property key file property))))))
 
 ;;;###tramp-autoload
 (defun tramp-flush-file-properties (key file)
diff --git a/lisp/net/tramp-cmds.el b/lisp/net/tramp-cmds.el
index a4f74383325..db3737500e6 100644
--- a/lisp/net/tramp-cmds.el
+++ b/lisp/net/tramp-cmds.el
@@ -632,13 +632,28 @@ For details, see `tramp-rename-files'."
   "Which method to be used in `tramp-file-name-with-sudo'."
   :group 'tramp
   :version "31.1"
+  ;; It should be a choice of constant strings.  See
+  ;; `with-tramp-file-name-with-method'.
   :type '(choice (const "su") (const "surs")
 		 (const "sudo") (const "sudors")
 		 (const "doas")
 		 (const "run0")
 		 (const "ksu"))
+  :initialize #'custom-initialize-default
+  :set #'tramp-set-file-name-with-method
   :link '(tramp-info-link :tag "Tramp manual" tramp-file-name-with-method))
 
+(defun tramp-set-file-name-with-method (symbol value)
+  "Set SYMBOL to value VALUE.
+Used in user option `tramp-file-name-with-method'.  If VALUE is an
+optional method, enable it."
+  (unless (string-equal (symbol-value symbol) value)
+    ;; Enable optional method.
+    (tramp-enable-method value)
+    ;; Set the value.
+    (when (assoc value tramp-methods)
+      (set-default symbol value))))
+
 (defun tramp-get-file-name-with-method ()
   "Return connection-local value of `tramp-file-name-with-method'."
   (tramp-compat-connection-local-value tramp-file-name-with-method))
@@ -651,8 +666,11 @@ Run BODY."
           (if current-prefix-arg
 	      (completing-read
 	       "Tramp method: "
-               (mapcar
-		#'cadr (cdr (get 'tramp-file-name-with-method 'custom-type)))
+	       ;; Filter out enabled methods.
+	       (seq-intersection
+		(mapcar #'car tramp-methods)
+		(mapcar
+		 #'cadr (cdr (get 'tramp-file-name-with-method 'custom-type))))
                nil t (tramp-get-file-name-with-method))
             (tramp-get-file-name-with-method))))
      ,@body))
diff --git a/lisp/net/tramp-compat.el b/lisp/net/tramp-compat.el
index 5d463bc0062..93190fec3a7 100644
--- a/lisp/net/tramp-compat.el
+++ b/lisp/net/tramp-compat.el
@@ -259,5 +259,8 @@ value is the default binding of the variable."
 ;;   instead of `condition-case' when the origin of an error shall be
 ;;   kept, for example when the HANDLER propagates the error with
 ;;   `(signal (car err) (cdr err)'.
+;;
+;; * Starting with Emacs 30.1, use '(_ VALUEFORM)' instead of
+;;   '(VALUEFORM)' in 'if-let*/when-let*/and-let*'.
 
 ;;; tramp-compat.el ends here
diff --git a/lisp/net/tramp-sh.el b/lisp/net/tramp-sh.el
index 98e3cae5a79..61f64e4c024 100644
--- a/lisp/net/tramp-sh.el
+++ b/lisp/net/tramp-sh.el
@@ -2934,15 +2934,15 @@ The method used must be an out-of-band method."
 	  ;; Try to insert the amount of free space.
 	  (goto-char (point-min))
 	  ;; First find the line to put it on.
-	  (when (and (search-forward-regexp
-		      (rx bol (group (* blank) "total")) nil t)
-		     ;; Emacs 29.1 or later.
-		     (not (fboundp 'dired--insert-disk-space)))
-	    (when-let* ((available (get-free-disk-space ".")))
-	      ;; Replace "total" with "total used", to avoid confusion.
-	      (replace-match "\\1 used in directory")
-	      (end-of-line)
-	      (insert " available " available))))
+	  (when-let* (((search-forward-regexp
+			(rx bol (group (* blank) "total")) nil t))
+		      ;; Emacs 29.1 or later.
+		      ((not (fboundp 'dired--insert-disk-space)))
+		      (available (get-free-disk-space ".")))
+	    ;; Replace "total" with "total used", to avoid confusion.
+	    (replace-match "\\1 used in directory")
+	    (end-of-line)
+	    (insert " available " available)))
 
 	(prog1 (goto-char end-marker)
 	  (set-marker beg-marker nil)
diff --git a/lisp/net/tramp.el b/lisp/net/tramp.el
index ec57aca0568..261fbc1139d 100644
--- a/lisp/net/tramp.el
+++ b/lisp/net/tramp.el
@@ -941,7 +941,7 @@ to be set, depending on VALUE."
   ;; Cleanup existing buffers.
   (unless (eq (symbol-value symbol) value)
     (tramp-cleanup-all-buffers))
-  ;; Set the value:
+  ;; Set the value.
   (set-default symbol value)
   ;; Reset the depending variables.
   (setq tramp-prefix-format (tramp-build-prefix-format)
@@ -4088,17 +4088,17 @@ BODY is the backend specific code."
 
 	   (let (last-coding-system-used (need-chown t))
 	     ;; Set file modification time.
-	     (when (or (eq ,visit t) (stringp ,visit))
-	       (when-let* ((file-attr (file-attributes filename 'integer)))
-		 (set-visited-file-modtime
-		  ;; We must pass modtime explicitly, because FILENAME
-		  ;; can be different from (buffer-file-name), f.e. if
-		  ;; `file-precious-flag' is set.
-		  (or (file-attribute-modification-time file-attr)
-		      (current-time)))
-		 (when (and (= (file-attribute-user-id file-attr) uid)
-			    (= (file-attribute-group-id file-attr) gid))
-		   (setq need-chown nil))))
+	     (when-let* (((or (eq ,visit t) (stringp ,visit)))
+			 (file-attr (file-attributes filename 'integer)))
+	       (set-visited-file-modtime
+		;; We must pass modtime explicitly, because FILENAME
+		;; can be different from (buffer-file-name), f.e. if
+		;; `file-precious-flag' is set.
+		(or (file-attribute-modification-time file-attr)
+		    (current-time)))
+	       (when (and (= (file-attribute-user-id file-attr) uid)
+			  (= (file-attribute-group-id file-attr) gid))
+		 (setq need-chown nil)))
 
 	     ;; Set the ownership.
              (when need-chown
@@ -7221,6 +7221,7 @@ Consults the auth-source package."
 		      (tramp-compat-auth-info-password auth-info))))
 
 	 ;; Try the password cache.
+	 ;; Starting with Emacs 31.1, this isn't needed anymore.
 	 (with-tramp-suspended-timers
 	   (setq auth-passwd
 		 (password-read
diff --git a/test/lisp/net/tramp-archive-resources/outer.zip b/test/lisp/net/tramp-archive-resources/foo.zip
similarity index 100%
rename from test/lisp/net/tramp-archive-resources/outer.zip
rename to test/lisp/net/tramp-archive-resources/foo.zip
diff --git a/test/lisp/net/tramp-archive-tests.el b/test/lisp/net/tramp-archive-tests.el
index ec56c4a0f93..5e9ea756b93 100644
--- a/test/lisp/net/tramp-archive-tests.el
+++ b/test/lisp/net/tramp-archive-tests.el
@@ -45,7 +45,7 @@
   "A directory file name, which looks like an archive.")
 
 (defvar tramp-archive-test-cascaded-file-archive
-  (ert-resource-file "outer.zip/foo.tar.gz")
+  (ert-resource-file "foo.zip/foo.tar.gz")
   "The cascaded test file archive.")
 
 (defvar tramp-archive-test-cascaded-archive
diff --git a/test/lisp/net/tramp-tests.el b/test/lisp/net/tramp-tests.el
index 3432e6eb706..2de753fb884 100644
--- a/test/lisp/net/tramp-tests.el
+++ b/test/lisp/net/tramp-tests.el
@@ -181,8 +181,11 @@ The temporary file is not created."
   `(condition-case err
        (progn ,@body)
      (file-error
-      (unless (string-equal (error-message-string err)
-			    "make-symbolic-link not supported")
+      (unless (string-match-p
+	       (rx bol (| "make-symbolic-link not supported"
+			  (: "Making symbolic link"
+			     (? ":") " Operation not permitted")))
+	       (error-message-string err))
 	(signal (car err) (cdr err))))))
 
 ;; Don't print messages in nested `tramp--test-instrument-test-case' calls.
@@ -8540,8 +8543,7 @@ process sentinels.  They shall not disturb each other."
 (ert-deftest tramp-test48-session-timeout ()
   "Check that Tramp handles a session timeout properly."
   (skip-unless (tramp--test-enabled))
-  (skip-unless
-   (tramp-get-method-parameter tramp-test-vec 'tramp-session-timeout))
+  (skip-unless (tramp--test-sh-p))
 
   ;; We want to see the timeout message.
   (tramp--test-instrument-test-case 3