--- a/m4/xstrtoimax.m4
+++ b/m4/xstrtoimax.m4
@@ -6,10 +6,11 @@
 AC_DEFUN([jm_AC_PREREQ_XSTRTOIMAX],
 [
   AC_REQUIRE([jm_AC_TYPE_INTMAX_T])
-  AC_REQUIRE([jm_AC_HEADER_INTTYPES_H])
+  AC_REQUIRE([jm_AC_TYPE_UINTMAX_T])
   AC_REQUIRE([jm_AC_TYPE_LONG_LONG])
+  AC_REQUIRE([jm_AC_TYPE_UNSIGNED_LONG_LONG])
   AC_CHECK_DECLS([strtol, strtoll])
-  AC_CHECK_HEADERS(limits.h stdlib.h)
+  AC_CHECK_HEADERS(limits.h stdlib.h inttypes.h)
 
   AC_CACHE_CHECK([whether <inttypes.h> defines strtoimax as a macro],
     jm_cv_func_strtoimax_macro,
@@ -24,27 +25,17 @@
     AC_REPLACE_FUNCS(strtoimax)
   fi
 
-  dnl We don't need (and can't compile) the replacement strtoll
-  dnl unless the type `long long' exists.
-  dnl Also, only the replacement strtoimax invokes strtoll,
-  dnl so we need the replacement strtoll only if strtoimax does not exist.
-  case "$ac_cv_type_long_long,$jm_cv_func_strtoimax_macro,$ac_cv_func_strtoimax" in
-    yes,no,no)
-      AC_REPLACE_FUNCS(strtoll)
+  dnl Only the replacement strtoimax invokes strtol and strtoll,
+  dnl so we need the replacements only if strtoimax does not exist.
+  case "$jm_cv_func_strtoimax_macro,$ac_cv_func_strtoimax" in
+    no,no)
+      AC_REPLACE_FUNCS(strtol)
 
-      dnl Check for strtol.  Mainly as a cue to cause automake to include
-      dnl strtol.c -- that file is included by each of strtoul.c and strtoull.c.
-      AC_REPLACE_FUNCS(strtol)
+      dnl We don't need (and can't compile) the replacement strtoll
+      dnl unless the type `long long' exists.
+      if test "$ac_cv_type_long_long" = yes; then
+	AC_REPLACE_FUNCS(strtoll)
+      fi
       ;;
   esac
-
-  case "$jm_cv_func_strtoimax_macro,$ac_cv_func_strtoimax" in
-    no,no)
-      AC_REPLACE_FUNCS(strtoul)
-
-      dnl See explanation above.
-      AC_REPLACE_FUNCS(strtol)
-      ;;
-  esac
-
 ])