diff --git a/doc/lispref/eval.texi b/doc/lispref/eval.texi
index 88e899de1e8..a45517287b7 100644
--- a/doc/lispref/eval.texi
+++ b/doc/lispref/eval.texi
@@ -252,11 +252,8 @@ the original symbol.  If the contents are another symbol, this
 process, called @dfn{symbol function indirection}, is repeated until
 it obtains a non-symbol.  @xref{Function Names}, for more information
 about symbol function indirection.
-
-  One possible consequence of this process is an infinite loop, in the
-event that a symbol's function cell refers to the same symbol.
-Otherwise, we eventually obtain a non-symbol, which ought to be a
-function or other suitable object.
+We eventually obtain a non-symbol, which ought to be a function or
+other suitable object.
 
 @kindex invalid-function
   More precisely, we should now have a Lisp function (a lambda
@@ -332,19 +329,17 @@ or just
   The built-in function @code{indirect-function} provides an easy way to
 perform symbol function indirection explicitly.
 
-@defun indirect-function function &optional noerror
+@defun indirect-function function
 @anchor{Definition of indirect-function}
 This function returns the meaning of @var{function} as a function.  If
 @var{function} is a symbol, then it finds @var{function}'s function
 definition and starts over with that value.  If @var{function} is not a
 symbol, then it returns @var{function} itself.
 
-This function returns @code{nil} if the final symbol is unbound.  It
-signals a @code{cyclic-function-indirection} error if there is a loop
-in the chain of symbols.
+This function returns @code{nil} if the final symbol is unbound.
 
-The optional argument @var{noerror} is obsolete, kept for backward
-compatibility, and has no effect.
+There is also a second, optional argument that is obsolete and has no
+effect.
 
 Here is how you could define @code{indirect-function} in Lisp:
 
diff --git a/doc/lispref/functions.texi b/doc/lispref/functions.texi
index f5572e447d3..b6a4ee13308 100644
--- a/doc/lispref/functions.texi
+++ b/doc/lispref/functions.texi
@@ -737,9 +737,12 @@ explicitly in the source file being loaded.  This is because
 By contrast, in programs that manipulate function definitions for other
 purposes, it is better to use @code{fset}, which does not keep such
 records.  @xref{Function Cells}.
+
+If the resulting function definition chain would be circular, then
+Emacs will signal a @code{cyclic-function-indirection} error.
 @end defun
 
-@defun function-alias-p object &optional noerror
+@defun function-alias-p object
 Checks whether @var{object} is a function alias.  If it is, it returns
 a list of symbols representing the function alias chain, else
 @code{nil}.  For instance, if @code{a} is an alias for @code{b}, and
@@ -750,9 +753,8 @@ a list of symbols representing the function alias chain, else
     @result{} (b c)
 @end example
 
-If there's a loop in the definitions, an error will be signaled.  If
-@var{noerror} is non-@code{nil}, the non-looping parts of the chain is
-returned instead.
+There is also a second, optional argument that is obsolete and has no
+effect.
 @end defun
 
   You cannot create a new primitive function with @code{defun} or
@@ -1539,6 +1541,9 @@ is not a function, e.g., a keyboard macro (@pxref{Keyboard Macros}):
 If you wish to use @code{fset} to make an alternate name for a
 function, consider using @code{defalias} instead.  @xref{Definition of
 defalias}.
+
+If the resulting function definition chain would be circular, then
+Emacs will signal a @code{cyclic-function-indirection} error.
 @end defun
 
 @node Closures
diff --git a/etc/NEWS b/etc/NEWS
index bcce416ebc1..4b0e4e6bd46 100644
--- a/etc/NEWS
+++ b/etc/NEWS
@@ -327,6 +327,21 @@ This function is like 'user-uid', but is aware of file name handlers,
 so it will return the remote UID for remote files (or -1 if the
 connection has no associated user).
 
++++
+** 'fset' and 'defalias' now signal an error for circular alias chains.
+Previously, 'fset' and 'defalias' could be made to build circular
+function indirection chains as in
+
+    (defalias 'able 'baker)
+    (defalias 'baker 'able)
+
+but trying to call them would often make Emacs hang.  Now, an attempt
+to create such a loop results in an error.
+
+Since circular alias chains now cannot occur, 'function-alias-p' and
+'indirect-function' will never signal an error.  Their second
+'noerror' arguments have no effect and are therefore obsolete.
+
 
 * Changes in Emacs 30.1 on Non-Free Operating Systems
 
diff --git a/lisp/help-fns.el b/lisp/help-fns.el
index 8bf8af73d30..1172f068934 100644
--- a/lisp/help-fns.el
+++ b/lisp/help-fns.el
@@ -996,7 +996,7 @@ Returns a list of the form (REAL-FUNCTION DEF ALIASED REAL-DEF)."
                                               (symbol-name function)))))))
 	 (real-def (cond
                     ((and aliased (not (subrp def)))
-                     (car (function-alias-p real-function t)))
+                     (car (function-alias-p real-function)))
 		    ((subrp def) (intern (subr-name def)))
                     (t def))))
 
diff --git a/lisp/subr.el b/lisp/subr.el
index 1a4ecc08931..916b6de494b 100644
--- a/lisp/subr.el
+++ b/lisp/subr.el
@@ -7002,27 +7002,17 @@ string will be displayed only if BODY takes longer than TIMEOUT seconds.
                                  (lambda ()
                                    ,@body)))
 
-(defun function-alias-p (func &optional noerror)
+(defun function-alias-p (func &optional _noerror)
   "Return nil if FUNC is not a function alias.
-If FUNC is a function alias, return the function alias chain.
-
-If the function alias chain contains loops, an error will be
-signaled.  If NOERROR, the non-loop parts of the chain is returned."
-  (declare (side-effect-free t))
-  (let ((chain nil)
-        (orig-func func))
-    (nreverse
-     (catch 'loop
-       (while (and (symbolp func)
-                   (setq func (symbol-function func))
-                   (symbolp func))
-         (when (or (memq func chain)
-                   (eq func orig-func))
-           (if noerror
-               (throw 'loop chain)
-             (signal 'cyclic-function-indirection (list orig-func))))
-         (push func chain))
-       chain))))
+If FUNC is a function alias, return the function alias chain."
+  (declare (advertised-calling-convention (func) "30.1")
+           (side-effect-free error-free))
+  (let ((chain nil))
+    (while (and (symbolp func)
+                (setq func (symbol-function func))
+                (symbolp func))
+      (push func chain))
+    (nreverse chain)))
 
 (defun readablep (object)
   "Say whether OBJECT has a readable syntax.
diff --git a/src/data.c b/src/data.c
index 1fa8b0358b5..d2f4d40d7bc 100644
--- a/src/data.c
+++ b/src/data.c
@@ -840,7 +840,9 @@ the position will be taken.  */)
 }
 
 DEFUN ("fset", Ffset, Sfset, 2, 2, 0,
-       doc: /* Set SYMBOL's function definition to DEFINITION, and return DEFINITION.  */)
+       doc: /* Set SYMBOL's function definition to DEFINITION, and return DEFINITION.
+If the resulting chain of function definitions would contain a loop,
+signal a `cyclic-function-indirection' error.  */)
   (register Lisp_Object symbol, Lisp_Object definition)
 {
   CHECK_SYMBOL (symbol);
@@ -852,6 +854,12 @@ DEFUN ("fset", Ffset, Sfset, 2, 2, 0,
 
   eassert (valid_lisp_object_p (definition));
 
+  /* Ensure non-circularity.  */
+  for (Lisp_Object s = definition; SYMBOLP (s) && !NILP (s);
+       s = XSYMBOL (s)->u.s.function)
+    if (EQ (s, symbol))
+      xsignal1 (Qcyclic_function_indirection, symbol);
+
 #ifdef HAVE_NATIVE_COMP
   register Lisp_Object function = XSYMBOL (symbol)->u.s.function;
 
@@ -1078,7 +1086,7 @@ If CMD is not a command, the return value is nil.
 Value, if non-nil, is a list (interactive SPEC).  */)
   (Lisp_Object cmd)
 {
-  Lisp_Object fun = indirect_function (cmd); /* Check cycles.  */
+  Lisp_Object fun = indirect_function (cmd);
   bool genfun = false;
 
   if (NILP (fun))
@@ -1168,7 +1176,7 @@ If COMMAND is not a command, the return value is nil.
 The value, if non-nil, is a list of mode name symbols.  */)
   (Lisp_Object command)
 {
-  Lisp_Object fun = indirect_function (command); /* Check cycles.  */
+  Lisp_Object fun = indirect_function (command);
 
   if (NILP (fun))
     return Qnil;
@@ -2482,55 +2490,22 @@ If the current binding is global (the default), the value is nil.  */)
 
 /* If OBJECT is a symbol, find the end of its function chain and
    return the value found there.  If OBJECT is not a symbol, just
-   return it.  If there is a cycle in the function chain, signal a
-   cyclic-function-indirection error.
-
-   This is like Findirect_function, except that it doesn't signal an
-   error if the chain ends up unbound.  */
+   return it.  */
 Lisp_Object
-indirect_function (register Lisp_Object object)
+indirect_function (Lisp_Object object)
 {
-  Lisp_Object tortoise, hare;
-
-  hare = tortoise = object;
-
-  for (;;)
-    {
-      if (!SYMBOLP (hare) || NILP (hare))
-	break;
-      hare = XSYMBOL (hare)->u.s.function;
-      if (!SYMBOLP (hare) || NILP (hare))
-	break;
-      hare = XSYMBOL (hare)->u.s.function;
-
-      tortoise = XSYMBOL (tortoise)->u.s.function;
-
-      if (EQ (hare, tortoise))
-	xsignal1 (Qcyclic_function_indirection, object);
-    }
-
-  return hare;
+  while (SYMBOLP (object) && !NILP (object))
+    object = XSYMBOL (object)->u.s.function;
+  return object;
 }
 
 DEFUN ("indirect-function", Findirect_function, Sindirect_function, 1, 2, 0,
        doc: /* Return the function at the end of OBJECT's function chain.
 If OBJECT is not a symbol, just return it.  Otherwise, follow all
-function indirections to find the final function binding and return it.
-Signal a cyclic-function-indirection error if there is a loop in the
-function chain of symbols.  */)
-  (register Lisp_Object object, Lisp_Object noerror)
+function indirections to find the final function binding and return it.  */)
+  (Lisp_Object object, Lisp_Object noerror)
 {
-  Lisp_Object result;
-
-  /* Optimize for no indirection.  */
-  result = object;
-  if (SYMBOLP (result) && !NILP (result)
-      && (result = XSYMBOL (result)->u.s.function, SYMBOLP (result)))
-    result = indirect_function (result);
-  if (!NILP (result))
-    return result;
-
-  return Qnil;
+  return indirect_function (object);
 }
 
 /* Extract and set vector and string elements.  */
diff --git a/src/eval.c b/src/eval.c
index e377e30c6fb..eb40c953f96 100644
--- a/src/eval.c
+++ b/src/eval.c
@@ -2116,7 +2116,7 @@ then strings and vectors are not accepted.  */)
 
   fun = function;
 
-  fun = indirect_function (fun); /* Check cycles.  */
+  fun = indirect_function (fun);
   if (NILP (fun))
     return Qnil;
 
diff --git a/test/lisp/help-fns-tests.el b/test/lisp/help-fns-tests.el
index 4d715cde1d5..243a45ae6d2 100644
--- a/test/lisp/help-fns-tests.el
+++ b/test/lisp/help-fns-tests.el
@@ -180,10 +180,6 @@ Return first line of the output of (describe-function-1 FUNC)."
 
 (ert-deftest help-fns--analyze-function-recursive ()
   (defalias 'help-fns--a 'help-fns--b)
-  (should (equal (help-fns--analyze-function 'help-fns--a)
-                 '(help-fns--a help-fns--b t help-fns--b)))
-  ;; Make a loop and see that it doesn't infloop.
-  (defalias 'help-fns--b 'help-fns--a)
   (should (equal (help-fns--analyze-function 'help-fns--a)
                  '(help-fns--a help-fns--b t help-fns--b))))
 
diff --git a/test/lisp/subr-tests.el b/test/lisp/subr-tests.el
index 1abd3be4ea1..d5efabc1370 100644
--- a/test/lisp/subr-tests.el
+++ b/test/lisp/subr-tests.el
@@ -1058,10 +1058,12 @@ final or penultimate step during initialization."))
                  '(subr-tests--b subr-tests--c)))
 
   (defalias 'subr-tests--d 'subr-tests--e)
-  (defalias 'subr-tests--e 'subr-tests--d)
-  (should-error (function-alias-p 'subr-tests--d))
-  (should (equal (function-alias-p 'subr-tests--d t)
-                 '(subr-tests--e))))
+  (should (equal (function-alias-p 'subr-tests--d)
+                 '(subr-tests--e)))
+
+  (fset 'subr-tests--f 'subr-tests--a)
+  (should (equal (function-alias-p 'subr-tests--f)
+                 '(subr-tests--a subr-tests--b subr-tests--c))))
 
 (ert-deftest test-readablep ()
   (should (readablep "foo"))
diff --git a/test/src/data-tests.el b/test/src/data-tests.el
index 28cee9d2c5b..680fdd57d71 100644
--- a/test/src/data-tests.el
+++ b/test/src/data-tests.el
@@ -772,4 +772,40 @@ comparing the subr with a much slower Lisp implementation."
   "Can't set variable marked with 'make_symbol_constant'."
   (should-error (setq most-positive-fixnum 1) :type 'setting-constant))
 
+(ert-deftest data-tests-fset ()
+  (fset 'data-tests--fs-fun (lambda () 'moo))
+  (declare-function data-tests--fs-fun nil)
+  (should (equal (data-tests--fs-fun) 'moo))
+
+  (fset 'data-tests--fs-fun1 'data-tests--fs-fun)
+  (declare-function data-tests--fs-fun1 nil)
+  (should (equal (data-tests--fs-fun1) 'moo))
+
+  (fset 'data-tests--fs-a 'data-tests--fs-b)
+  (fset 'data-tests--fs-b 'data-tests--fs-c)
+
+  (should-error (fset 'data-tests--fs-c 'data-tests--fs-c)
+                :type 'cyclic-function-indirection)
+  (fset 'data-tests--fs-d 'data-tests--fs-a)
+  (should-error (fset 'data-tests--fs-c 'data-tests--fs-d)
+                :type 'cyclic-function-indirection))
+
+(ert-deftest data-tests-defalias ()
+  (defalias 'data-tests--da-fun (lambda () 'baa))
+  (declare-function data-tests--da-fun nil)
+  (should (equal (data-tests--da-fun) 'baa))
+
+  (defalias 'data-tests--da-fun1 'data-tests--da-fun)
+  (declare-function data-tests--da-fun1 nil)
+  (should (equal (data-tests--da-fun1) 'baa))
+
+  (defalias 'data-tests--da-a 'data-tests--da-b)
+  (defalias 'data-tests--da-b 'data-tests--da-c)
+
+  (should-error (defalias 'data-tests--da-c 'data-tests--da-c)
+                :type 'cyclic-function-indirection)
+  (defalias 'data-tests--da-d 'data-tests--da-a)
+  (should-error (defalias 'data-tests--da-c 'data-tests--da-d)
+                :type 'cyclic-function-indirection))
+
 ;;; data-tests.el ends here