diff --git a/NEWS b/NEWS
index fbf9f4cc..35a561d9 100644
--- a/NEWS
+++ b/NEWS
@@ -69,7 +69,11 @@ GNU Bison NEWS
 
   Bison templates now prefer signed to unsigned integer types when
   either will do, as the signed types are less error-prone and allow
-  for better checking with 'gcc -fsanitize=undefined'.
+  for better checking with 'gcc -fsanitize=undefined'.  Also, the
+  types chosen are now portable to unusual machines where char, short and
+  int are all the same width.  On non-GNU platforms this may entail
+  including <limits.h> and (if available) <stdint.h> to define integer types
+  and constants.
 
 * Noteworthy changes in release 3.4.2 (2019-09-12) [stable]
 
diff --git a/data/skeletons/yacc.c b/data/skeletons/yacc.c
index 10708627..8d32af56 100644
--- a/data/skeletons/yacc.c
+++ b/data/skeletons/yacc.c
@@ -114,7 +114,7 @@ m4_ifset([b4_parse_param], [b4_args(b4_parse_param), ])])
 # ---------------------
 # Return a narrow int type able to handle numbers ranging from
 # MIN to MAX (included).  Overwrite the version from c.m4,
-# so that the user can override the shorter types.
+# so that the code can use C99 types if available.
 m4_define([b4_int_type],
 [m4_if(b4_ints_in($@,   [-127],   [127]), [1], [yytype_int8],
        b4_ints_in($@,      [0],   [255]), [1], [yytype_uint8],
@@ -388,26 +388,54 @@ m4_if(b4_api_prefix, [yy], [],
 # undef short
 #endif
 
-#ifdef YYTYPE_UINT8
-typedef YYTYPE_UINT8 yytype_uint8;
-#else
-typedef unsigned char yytype_uint8;
+/* On compilers that do not define __PTRDIFF_MAX__ etc., include
+   <limits.h> and (if available) <stdint.h> so that the code can
+   choose integer types of a good width.  */
+
+#ifndef __PTRDIFF_MAX__
+# include <limits.h> /* INFRINGES ON USER NAME SPACE */
+# if defined __STDC_VERSION__ && 199901 <= __STDC_VERSION__
+#  include <stdint.h> /* INFRINGES ON USER NAME SPACE */
+# endif
 #endif
 
-#ifdef YYTYPE_INT8
-typedef YYTYPE_INT8 yytype_int8;
+/* Narrow types that promote to a signed type and that can represent a
+   signed or unsigned integer of at least N bits.  In tables they can
+   save space and decrease cache pressure.  Promoting to a signed type
+   helps avoid bugs in integer arithmetic.  */
+
+#if defined __UINT_LEAST8_MAX__ && __UINT_LEAST8_MAX__ <= __INT_MAX__
+typedef __UINT_LEAST8_TYPE__ yytype_uint8;
+#elif defined UINT_LEAST8_MAX && UINT_LEAST8_MAX <= INT_MAX
+typedef uint_least8_t yytype_uint8;
+#elif UCHAR_MAX <= INT_MAX
+typedef unsigned char yytype_uint8;
+#else
+typedef short yytype_uint8;
+#endif
+
+#if defined __INT_LEAST8_MAX__ && __INT_LEAST8_MAX__ <= __INT_MAX__
+typedef __INT_LEAST8_TYPE__ yytype_int8;
+#elif defined INT_LEAST8_MAX && INT_LEAST8_MAX <= INT_MAX
+typedef int_least8_t yytype_int8;
 #else
 typedef signed char yytype_int8;
 #endif
 
-#ifdef YYTYPE_UINT16
-typedef YYTYPE_UINT16 yytype_uint16;
-#else
+#if defined __UINT_LEAST16_MAX__ && __UINT_LEAST16_MAX__ <= __INT_MAX__
+typedef __UINT_LEAST16_TYPE__ yytype_uint16;
+#elif defined UINT_LEAST16_MAX && UINT_LEAST16_MAX <= INT_MAX
+typedef uint_least16_t yytype_uint16;
+#elif USHRT_MAX <= INT_MAX
 typedef unsigned short yytype_uint16;
+#else
+typedef int yytype_uint16;
 #endif
 
-#ifdef YYTYPE_INT16
-typedef YYTYPE_INT16 yytype_int16;
+#if defined __INT_LEAST16_MAX__ && __INT_LEAST16_MAX__ <= __INT_MAX__
+typedef __INT_LEAST16_TYPE__ yytype_int16;
+#elif defined INT_LEAST16_MAX && INT_LEAST16_MAX <= INT_MAX
+typedef int_least16_t yytype_int16;
 #else
 typedef short yytype_int16;
 #endif
@@ -416,17 +444,14 @@ typedef short yytype_int16;
 # if defined __PTRDIFF_TYPE__ && defined __PTRDIFF_MAX__
 #  define YYPTRDIFF_T __PTRDIFF_TYPE__
 #  define YYPTRDIFF_MAXIMUM __PTRDIFF_MAX__
-# elif defined ptrdiff_t && defined PTRDIFF_MAX
+# elif defined PTRDIFF_MAX
+#  ifndef ptrdiff_t
+#   include <stddef.h> /* INFRINGES ON USER NAME SPACE */
+#  endif
 #  define YYPTRDIFF_T ptrdiff_t
 #  define YYPTRDIFF_MAXIMUM PTRDIFF_MAX
-# elif defined __STDC_VERSION__ && 199901 <= __STDC_VERSION__
-#  include <stddef.h> /* INFRINGES ON USER NAME SPACE */
-#  define YYPTRDIFF_T ptrdiff_t
-#  include <stdint.h> /* INFRINGES ON USER NAME SPACE */
-#  define YYPTRDIFF_MAXIMUM PTRDIFF_MAX
 # else
 #  define YYPTRDIFF_T long
-#  include <limits.h> /* INFRINGES ON USER NAME SPACE */
 #  define YYPTRDIFF_MAXIMUM LONG_MAX
 # endif
 #endif
diff --git a/doc/bison.texi b/doc/bison.texi
index 6f4ca9e2..c78bd31e 100644
--- a/doc/bison.texi
+++ b/doc/bison.texi
@@ -1447,13 +1447,13 @@ anything other than their usual meanings.
 
 In some cases the Bison parser implementation file includes system
 headers, and in those cases your code should respect the identifiers
-reserved by those headers.  On some non-GNU hosts, @code{<alloca.h>},
-@code{<malloc.h>}, @code{<stddef.h>}, and @code{<stdlib.h>} are
-included as needed to declare memory allocators and related types.
+reserved by those headers.  On some non-GNU hosts, @code{<limits.h>},
+@code{<stddef.h>}, @code{<stdint.h>} (if available), and @code{<stdlib.h>}
+are included to declare memory allocators and integer types and constants.
 @code{<libintl.h>} is included if message translation is in use
 (@pxref{Internationalization}).  Other system headers may be included
-if you define @code{YYDEBUG} to a nonzero value (@pxref{Tracing,
-,Tracing Your Parser}).
+if you define @code{YYDEBUG} (@pxref{Tracing, ,Tracing Your Parser}) or
+@code{YYSTACK_USE_ALLOCA} (@pxref{Table of Symbols}) to a nonzero value.
 
 @node Stages
 @section Stages in Using Bison
diff --git a/src/parse-gram.y b/src/parse-gram.y
index b4132841..043fa581 100644
--- a/src/parse-gram.y
+++ b/src/parse-gram.y
@@ -112,11 +112,6 @@
   /* A string that describes a char (e.g., 'a' -> "'a'").  */
   static char const *char_name (char);
 
-  #define YYTYPE_INT16 int_fast16_t
-  #define YYTYPE_INT8 int_fast8_t
-  #define YYTYPE_UINT16 uint_fast16_t
-  #define YYTYPE_UINT8 uint_fast8_t
-
   /* Add style to semantic values in traces.  */
   static void tron (FILE *yyo);
   static void troff (FILE *yyo);