diff --git a/lisp/subr.el b/lisp/subr.el
index 9d251045881..cad15f90c8a 100644
--- a/lisp/subr.el
+++ b/lisp/subr.el
@@ -2145,6 +2145,9 @@ instead; it will indirectly limit the specpdl stack size as well.")
   "Add to the value of HOOK the function FUNCTION.
 FUNCTION is not added if already present.
 
+HOOK should be a symbol.  If HOOK is void, or if HOOK's value is a
+single function, it is changed to a list of functions.
+
 The place where the function is added depends on the DEPTH
 parameter.  DEPTH defaults to 0.  By convention, it should be
 a number between -100 and 100 where 100 means that the function
@@ -2163,10 +2166,6 @@ This makes the hook buffer-local, and it makes t a member of the
 buffer-local value.  That acts as a flag to run the hook
 functions of the global value as well as in the local value.
 
-HOOK should be a symbol.  If HOOK is void, it is first set to
-nil.  If HOOK's value is a single function, it is changed to a
-list of functions.
-
 FUNCTION may be any valid function, but it's recommended to use a
 function symbol and not a lambda form.  Using a symbol will
 ensure that the function is not re-added if the function is
@@ -2231,10 +2230,11 @@ performance impact when running `add-hook' and `remove-hook'."
       (set-default hook hook-value))))
 
 (defun remove-hook (hook function &optional local)
-  "Remove from the value of HOOK the function FUNCTION.
-HOOK should be a symbol, and FUNCTION may be any valid function.  If
-FUNCTION isn't the value of HOOK, or, if FUNCTION doesn't appear in the
-list of hooks to run in HOOK, then nothing is done.  See `add-hook'.
+  "Remove FUNCTION from HOOK's functions.
+HOOK should be a symbol, and FUNCTION may be any valid function.
+Do nothing if HOOK does not currently contain FUNCTION.
+Compare functions with `equal`, which means that it can be
+slow if FUNCTION is not a symbol.  See `add-hook'.
 
 The optional third argument, LOCAL, if non-nil, says to modify
 the hook's buffer-local value rather than its default value.
diff --git a/src/fns.c b/src/fns.c
index 329a4e124b3..62283e92eb7 100644
--- a/src/fns.c
+++ b/src/fns.c
@@ -6320,6 +6320,11 @@ command `prefer-coding-system') is used.
 If NOERROR is non-nil, silently assume the `raw-text' coding if the
 guesswork fails.  Normally, an error is signaled in such case.
 
+This function is semi-obsolete, since for most purposes it is equivalent
+to calling `secure-hash` with the symbol `md5' as the ALGORITHM
+argument.  The OBJECT, START and END arguments have the same meanings as
+in `secure-hash'.
+
 Note that MD5 is not collision resistant and should not be used for
 anything security-related.  See `secure-hash' for alternatives.  */)
   (Lisp_Object object, Lisp_Object start, Lisp_Object end, Lisp_Object coding_system, Lisp_Object noerror)