diff --git a/docs/reference/constrained.rst b/docs/reference/constrained.rst
index 8d3ba0e3af..8b64fd98fc 100644
--- a/docs/reference/constrained.rst
+++ b/docs/reference/constrained.rst
@@ -112,7 +112,8 @@ with an underscore as in ``_COLS``: this symbol is not visible outside the
 module so will not occupy RAM.
 
 The argument to ``const()`` may be anything which, at compile time, evaluates
-to an integer e.g. ``0x100`` or ``1 << 8``. It can even include other const
+to a constant e.g. ``0x100``, ``1 << 8`` or ``(True, "string", b"bytes")``
+(see section below for details).  It can even include other const
 symbols that have already been defined, e.g. ``1 << BIT``.
 
 **Constant data structures**
diff --git a/py/parse.c b/py/parse.c
index b8a40f4bb5..3972893cbb 100644
--- a/py/parse.c
+++ b/py/parse.c
@@ -357,7 +357,7 @@ bool mp_parse_node_get_int_maybe(mp_parse_node_t pn, mp_obj_t *o) {
     }
 }
 
-#if MICROPY_COMP_CONST_TUPLE
+#if MICROPY_COMP_CONST_TUPLE || MICROPY_COMP_CONST
 STATIC bool mp_parse_node_is_const(mp_parse_node_t pn) {
     if (MP_PARSE_NODE_IS_SMALL_INT(pn)) {
         // Small integer.
@@ -545,9 +545,9 @@ STATIC mp_parse_node_t make_node_const_object(parser_t *parser, size_t src_line,
     return (mp_parse_node_t)pn;
 }
 
-// Create a parse node represeting a constant integer value, possibly optimising
-// it by putting the (small) integer value directly in the parse node itself.
-STATIC mp_parse_node_t make_node_const_int(parser_t *parser, size_t src_line, mp_obj_t obj) {
+// Create a parse node represeting a constant object, possibly optimising the case of
+// an integer, by putting the (small) integer value directly in the parse node itself.
+STATIC mp_parse_node_t make_node_const_object_optimised(parser_t *parser, size_t src_line, mp_obj_t obj) {
     if (mp_obj_is_small_int(obj)) {
         mp_int_t val = MP_OBJ_SMALL_INT_VALUE(obj);
         #if MICROPY_OBJ_REPR == MICROPY_OBJ_REPR_D
@@ -579,7 +579,7 @@ STATIC void push_result_token(parser_t *parser, uint8_t rule_id) {
         mp_map_elem_t *elem;
         if (rule_id == RULE_atom
             && (elem = mp_map_lookup(&parser->consts, MP_OBJ_NEW_QSTR(id), MP_MAP_LOOKUP)) != NULL) {
-            pn = make_node_const_int(parser, lex->tok_line, elem->value);
+            pn = make_node_const_object_optimised(parser, lex->tok_line, elem->value);
         } else {
             pn = mp_parse_node_new_leaf(MP_PARSE_NODE_ID, id);
         }
@@ -589,7 +589,7 @@ STATIC void push_result_token(parser_t *parser, uint8_t rule_id) {
         #endif
     } else if (lex->tok_kind == MP_TOKEN_INTEGER) {
         mp_obj_t o = mp_parse_num_integer(lex->vstr.buf, lex->vstr.len, 0, lex);
-        pn = make_node_const_int(parser, lex->tok_line, o);
+        pn = make_node_const_object_optimised(parser, lex->tok_line, o);
     } else if (lex->tok_kind == MP_TOKEN_FLOAT_OR_IMAG) {
         mp_obj_t o = mp_parse_num_decimal(lex->vstr.buf, lex->vstr.len, true, false, lex);
         pn = make_node_const_object(parser, lex->tok_line, o);
@@ -803,14 +803,14 @@ STATIC bool fold_constants(parser_t *parser, uint8_t rule_id, size_t num_args) {
 
                 // get the value
                 mp_parse_node_t pn_value = ((mp_parse_node_struct_t *)((mp_parse_node_struct_t *)pn1)->nodes[1])->nodes[0];
-                mp_obj_t value;
-                if (!mp_parse_node_get_int_maybe(pn_value, &value)) {
+                if (!mp_parse_node_is_const(pn_value)) {
                     mp_obj_t exc = mp_obj_new_exception_msg(&mp_type_SyntaxError,
-                        MP_ERROR_TEXT("constant must be an integer"));
+                        MP_ERROR_TEXT("not a constant"));
                     mp_obj_exception_add_traceback(exc, parser->lexer->source_name,
                         ((mp_parse_node_struct_t *)pn1)->source_line, MP_QSTRnull);
                     nlr_raise(exc);
                 }
+                mp_obj_t value = mp_parse_node_convert_to_obj(pn_value);
 
                 // store the value in the table of dynamic constants
                 mp_map_elem_t *elem = mp_map_lookup(&parser->consts, MP_OBJ_NEW_QSTR(id), MP_MAP_LOOKUP_ADD_IF_NOT_FOUND);
@@ -872,7 +872,7 @@ STATIC bool fold_constants(parser_t *parser, uint8_t rule_id, size_t num_args) {
     for (size_t i = num_args; i > 0; i--) {
         pop_result(parser);
     }
-    push_result_node(parser, make_node_const_int(parser, 0, arg0));
+    push_result_node(parser, make_node_const_object_optimised(parser, 0, arg0));
 
     return true;
 }
diff --git a/tests/micropython/const_alltypes.py b/tests/micropython/const_alltypes.py
new file mode 100644
index 0000000000..b5f36edc4f
--- /dev/null
+++ b/tests/micropython/const_alltypes.py
@@ -0,0 +1,26 @@
+# Test constant optimisation, with full range of const types.
+# This test will only work when MICROPY_COMP_CONST and MICROPY_COMP_CONST_TUPLE are enabled.
+
+from micropython import const
+
+_INT = const(123)
+_STR = const("str")
+_BYTES = const(b"bytes")
+_TUPLE = const((_INT, _STR, _BYTES))
+_TUPLE2 = const((None, False, True, ..., (), _TUPLE))
+
+print(_INT)
+print(_STR)
+print(_BYTES)
+print(_TUPLE)
+print(_TUPLE2)
+
+x = _TUPLE
+print(x is _TUPLE)
+print(x is (_INT, _STR, _BYTES))
+
+print(hasattr(globals(), "_INT"))
+print(hasattr(globals(), "_STR"))
+print(hasattr(globals(), "_BYTES"))
+print(hasattr(globals(), "_TUPLE"))
+print(hasattr(globals(), "_TUPLE2"))
diff --git a/tests/micropython/const_alltypes.py.exp b/tests/micropython/const_alltypes.py.exp
new file mode 100644
index 0000000000..77aeffffab
--- /dev/null
+++ b/tests/micropython/const_alltypes.py.exp
@@ -0,0 +1,12 @@
+123
+str
+b'bytes'
+(123, 'str', b'bytes')
+(None, False, True, Ellipsis, (), (123, 'str', b'bytes'))
+True
+True
+False
+False
+False
+False
+False