diff --git a/Doc/c-api/arg.rst b/Doc/c-api/arg.rst
index 58456a36b96c151..a878b20c928ea3d 100644
--- a/Doc/c-api/arg.rst
+++ b/Doc/c-api/arg.rst
@@ -399,13 +399,18 @@ inside nested parentheses.  They are:
    their default value --- when an optional argument is not specified,
    :c:func:`PyArg_ParseTuple` does not touch the contents of the corresponding C
    variable(s).
+   For example, the format string ``"OO|OO"`` corresponds to the Python
+   signature ``f(a, b, c=None, d=None)``.
 
 ``$``
    :c:func:`PyArg_ParseTupleAndKeywords` only:
    Indicates that the remaining arguments in the Python argument list are
-   keyword-only.  Currently, all keyword-only arguments must also be optional
-   arguments, so ``|`` must always be specified before ``$`` in the format
-   string.
+   keyword-only.
+   They are optional if ``|`` was specified before ``$``, and required otherwise.
+   ``|`` cannot be specified after ``$``.
+   For example, the format string ``"O|O$O"`` corresponds to the Python
+   signature ``f(a, b=None, *, c=None)``,
+   and the format string ``"OO$OO"`` corresponds to ``f(a, b, *, c, d)``.
 
    .. versionadded:: 3.3
 
diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index 619d0cb2fe541a6..2875303fb156197 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -9806,6 +9806,7 @@ def test_order_in_union(self):
         for args in itertools.permutations(get_args(expr1)):
             with self.subTest(args=args):
                 self.assertEqual(expr1, reduce(operator.or_, args))
+                self.assertEqual(expr1, Union[args])
 
         expr2 = Union[Annotated[int, 1], str, Annotated[str, {}], int]
         for args in itertools.permutations(get_args(expr2)):
diff --git a/Lib/typing.py b/Lib/typing.py
index 809c0ff88607a59..b56ba954ad38be1 100644
--- a/Lib/typing.py
+++ b/Lib/typing.py
@@ -494,7 +494,7 @@ def _eval_type(t, globalns, localns, type_params, *, recursive_guard=frozenset()
         if isinstance(t, GenericAlias):
             return _rebuild_generic_alias(t, ev_args)
         if isinstance(t, Union):
-            return functools.reduce(operator.or_, ev_args)
+            return Union[ev_args]
         else:
             return t.copy_with(ev_args)
     return t
@@ -2546,7 +2546,7 @@ def _strip_annotations(t):
         stripped_args = tuple(_strip_annotations(a) for a in t.__args__)
         if stripped_args == t.__args__:
             return t
-        return functools.reduce(operator.or_, stripped_args)
+        return Union[stripped_args]
 
     return t