diff --git a/m4/gnulib-common.m4 b/m4/gnulib-common.m4
index 57343e440..4443a99ce 100644
--- a/m4/gnulib-common.m4
+++ b/m4/gnulib-common.m4
@@ -1,4 +1,4 @@
-# gnulib-common.m4 serial 60
+# gnulib-common.m4 serial 61
 dnl Copyright (C) 2007-2020 Free Software Foundation, Inc.
 dnl This file is free software; the Free Software Foundation
 dnl gives unlimited permission to copy and/or distribute it,
@@ -483,7 +483,11 @@ AC_DEFUN([gl_FEATURES_H],
 # gl_PROG_CC_C99
 # Modifies the value of the shell variable CC in an attempt to make $CC
 # understand ISO C99 source code.
-# This is like AC_PROG_CC_C99, except that
+# This macro's implementation is not quite right, since it attempts to
+# use the latest version of the C standard instead of using C99 only.
+# So far there has seemed little motivation to fix this, as later standards
+# have mostly been extensions to C99.
+# With Autoconf 2.69 and earlier this is like AC_PROG_CC_C99, except that
 # - AC_PROG_CC_C99 does not mix well with AC_PROG_CC_STDC
 #   <https://lists.gnu.org/r/bug-gnulib/2011-09/msg00367.html>,
 #   but many more packages use AC_PROG_CC_STDC than AC_PROG_CC_C99
@@ -495,10 +499,8 @@ AC_DEFUN([gl_FEATURES_H],
 # - AC_PROG_CC_STDC is likely to change now that C11 is an ISO standard.
 AC_DEFUN([gl_PROG_CC_C99],
 [
-  dnl Change that version number to the minimum Autoconf version that supports
-  dnl mixing AC_PROG_CC_C99 calls with AC_PROG_CC_STDC calls.
-  m4_version_prereq([9.0],
-    [AC_REQUIRE([AC_PROG_CC_C99])],
+  m4_version_prereq([2.69.301-14265], dnl Change to 2.70 when 2.70 comes out.
+    [AC_REQUIRE([AC_PROG_CC])],
     [AC_REQUIRE([AC_PROG_CC_STDC])])
 ])
 
diff --git a/m4/malloc.m4 b/m4/malloc.m4
index c1f8ea32f..c6d814220 100644
--- a/m4/malloc.m4
+++ b/m4/malloc.m4
@@ -15,7 +15,7 @@ AC_DEFUN([_AC_FUNC_MALLOC_IF],
     [ac_cv_func_malloc_0_nonnull],
     [AC_RUN_IFELSE(
        [AC_LANG_PROGRAM(
-          [[#if defined STDC_HEADERS || defined HAVE_STDLIB_H
+          [[#ifdef HAVE_STDLIB_H
             # include <stdlib.h>
             #else
             char *malloc ();
diff --git a/m4/realloc.m4 b/m4/realloc.m4
index 85b8f874f..561e98823 100644
--- a/m4/realloc.m4
+++ b/m4/realloc.m4
@@ -15,7 +15,7 @@ AC_DEFUN([_AC_FUNC_REALLOC_IF],
     [ac_cv_func_realloc_0_nonnull],
     [AC_RUN_IFELSE(
        [AC_LANG_PROGRAM(
-          [[#if defined STDC_HEADERS || defined HAVE_STDLIB_H
+          [[#ifdef HAVE_STDLIB_H
             # include <stdlib.h>
             #else
             char *realloc ();