diff --git a/lisp/gnus/gnus-fun.el b/lisp/gnus/gnus-fun.el
index fa78b5c6e15..a6b27300233 100644
--- a/lisp/gnus/gnus-fun.el
+++ b/lisp/gnus/gnus-fun.el
@@ -44,7 +44,7 @@
   "Regexp to match faces in `gnus-x-face-directory' to be omitted."
   :version "25.1"
   :group 'gnus-fun
-  :type 'string)
+  :type '(choice (const nil) string))
 
 (defcustom gnus-face-directory (expand-file-name "faces" gnus-directory)
   "*Directory where Face PNG files are stored."
@@ -56,7 +56,7 @@
   "Regexp to match faces in `gnus-face-directory' to be omitted."
   :version "25.1"
   :group 'gnus-fun
-  :type 'string)
+  :type '(choice (const nil) string))
 
 (defcustom gnus-convert-pbm-to-x-face-command "pbmtoxbm %s | compface"
   "Command for converting a PBM to an X-Face."
diff --git a/lisp/gnus/gnus.el b/lisp/gnus/gnus.el
index 1196ea9dfec..5d2ce7ee19f 100644
--- a/lisp/gnus/gnus.el
+++ b/lisp/gnus/gnus.el
@@ -1637,6 +1637,7 @@ this variable.  I think."
 					     (const post-mail))
 			(checklist :inline t :greedy t
 				   (const :format "%v " address)
+				   (const cloud)
 				   (const global)
 				   (const :format "%v " prompt-address)
 				   (const :format "%v " physical-address)
diff --git a/lisp/mail/rmail.el b/lisp/mail/rmail.el
index 9a03b0516df..390ca3fad52 100644
--- a/lisp/mail/rmail.el
+++ b/lisp/mail/rmail.el
@@ -692,8 +692,9 @@ Element N specifies the summary line for message N+1.")
 This is set to nil by default.")
 
 (defcustom rmail-get-coding-function nil
-  "Function of no args to try to determine coding system for a message."
-  :type 'function
+  "Function of no args to try to determine coding system for a message.
+If nil, just search for `rmail-mime-charset-pattern'."
+  :type '(choice (const nil) function)
   :group 'rmail
   :version "24.4")
 
diff --git a/lisp/net/newst-treeview.el b/lisp/net/newst-treeview.el
index 0e75236154b..4de3d1d1125 100644
--- a/lisp/net/newst-treeview.el
+++ b/lisp/net/newst-treeview.el
@@ -132,9 +132,9 @@ Example: (\"Topmost group\" \"feed1\" (\"subgroup1\" \"feed 2\")
 
 (defcustom newsticker-groups-filename
   nil
-  "Name of the newsticker groups settings file.  This variable is obsolete."
+  "Name of the newsticker groups settings file."
   :version "25.1"                       ; changed default value to nil
-  :type 'string
+  :type '(choice (const nil) string)
   :group 'newsticker-treeview)
 (make-obsolete-variable 'newsticker-groups-filename 'newsticker-dir "23.1")
 
diff --git a/lisp/progmodes/hideif.el b/lisp/progmodes/hideif.el
index 43cf42c048b..cc7d1c368c5 100644
--- a/lisp/progmodes/hideif.el
+++ b/lisp/progmodes/hideif.el
@@ -138,7 +138,7 @@
 
 (defcustom hide-ifdef-exclude-define-regexp nil
   "Ignore #define names if those names match this exclusion pattern."
-  :type 'string
+  :type '(choice (const nil) string)
   :version "25.1")
 
 (defcustom hide-ifdef-expand-reinclusion-protection t
diff --git a/lisp/textmodes/tildify.el b/lisp/textmodes/tildify.el
index eb799c09510..598060e9ec8 100644
--- a/lisp/textmodes/tildify.el
+++ b/lisp/textmodes/tildify.el
@@ -417,7 +417,7 @@ current `case-fold-search' setting."
   "A list of predicate functions for `tildify-space' function."
   :version "25.1"
   :group 'tildify
-  :type '(repeat 'function))
+  :type '(repeat function))
 
 (defcustom tildify-double-space-undos t
   "Weather `tildify-space' should undo hard space when space is typed again."
diff --git a/lisp/url/url-tramp.el b/lisp/url/url-tramp.el
index 9e191579d47..192a0459f33 100644
--- a/lisp/url/url-tramp.el
+++ b/lisp/url/url-tramp.el
@@ -30,11 +30,11 @@
 
 ;;;###autoload
 (defcustom url-tramp-protocols '("ftp" "ssh" "scp" "rsync" "telnet")
-  "List of URL protocols the work is handled by Tramp.
+  "List of URL protocols for which the work is handled by Tramp.
 They must also be covered by `url-handler-regexp'."
   :group 'url
   :version "25.1"
-  :type '(list string))
+  :type '(repeat string))
 
 (defun url-tramp-convert-url-to-tramp (url)
   "Convert URL to a Tramp file name."