diff --git a/doc/misc/url.texi b/doc/misc/url.texi
index 91cb6b54a847..b5e6e2ce465a 100644
--- a/doc/misc/url.texi
+++ b/doc/misc/url.texi
@@ -221,6 +221,7 @@ URI Encoding
 @section URI Encoding
 
 @cindex percent encoding
+@findex url-generic-parse-url
   The @code{url-generic-parse-url} parser does not obey RFC 3986 in
 one respect: it allows non-@acronym{ASCII} characters in URI strings.
 
@@ -233,6 +234,7 @@ URI Encoding
 @acronym{ASCII} characters must also be percent encoded when they
 appear in URI components.)
 
+@findex url-encode-url
   The function @code{url-encode-url} can be used to convert a URI
 string containing arbitrary characters to one that is properly
 percent-encoded in accordance with RFC 3986.
@@ -244,11 +246,13 @@ URI Encoding
 previously uppercase.
 @end defun
 
+@findex url-hexify-string
+@findex url-unhex-string
   To convert between a string containing arbitrary characters and a
 percent-encoded all-@acronym{ASCII} string, use the functions
 @code{url-hexify-string} and @code{url-unhex-string}:
 
-@defun url-hexify-string string &optional allowed-chars
+@defun url-hexify-string string &optional allowed-chars list-chars
 This function performs percent-encoding on @var{string}, and returns
 the result.
 
diff --git a/lisp/url/url-util.el b/lisp/url/url-util.el
index 1ae2213eee65..96fc741a1700 100644
--- a/lisp/url/url-util.el
+++ b/lisp/url/url-util.el
@@ -398,18 +398,23 @@ url--allowed-chars
     vec))
 
 ;;;###autoload
-(defun url-hexify-string (string &optional allowed-chars)
+(defun url-hexify-string (string &optional allowed-chars list-chars)
   "URI-encode STRING and return the result.
 If STRING is multibyte, it is first converted to a utf-8 byte
 string.  Each byte corresponding to an allowed character is left
 as-is, while all other bytes are converted to a three-character
 string: \"%\" followed by two upper-case hex digits.
 
-The allowed characters are specified by ALLOWED-CHARS.  If this
+The allowed characters are specified by ALLOWED-CHARS. If this
 argument is nil, the list `url-unreserved-chars' determines the
-allowed characters.  Otherwise, ALLOWED-CHARS should be a vector
-whose Nth element is non-nil if character N is allowed."
-  (unless allowed-chars
+allowed characters.  Otherwise, if LIST-CHARS is nil or omitted,
+ALLOWED-CHARS should be a vector whose Nth element is non-nil if
+character N is allowed; if LIST-CHARS is non-nil, ALLOWED-CHARS
+should be a list of allowed chars.
+"
+  (if allowed-chars
+      (when list-chars
+        (setq allowed-chars (url--allowed-chars allowed-chars)))
     (setq allowed-chars (url--allowed-chars url-unreserved-chars)))
   (mapconcat (lambda (byte)
 	       (if (aref allowed-chars byte)