diff --git a/pep-0539.txt b/pep-0539.txt
index 143ee3ed7..d7bba3677 100644
--- a/pep-0539.txt
+++ b/pep-0539.txt
@@ -52,12 +52,12 @@ These would be superseded by a new set of analogous functions::
 
     PyAPI_FUNC(int) PyThread_tss_create(Py_tss_t *key)
     PyAPI_FUNC(void) PyThread_tss_delete(Py_tss_t *key)
-    PyAPI_FUNC(int) PyThread_tss_set(Py_tss_t key, void *value)
-    PyAPI_FUNC(void *) PyThread_tss_get(Py_tss_t key)
-    PyAPI_FUNC(void) PyThread_tss_delete_value(Py_tss_t key)
+    PyAPI_FUNC(int) PyThread_tss_set(Py_tss_t *key, void *value)
+    PyAPI_FUNC(void *) PyThread_tss_get(Py_tss_t *key)
+    PyAPI_FUNC(void) PyThread_tss_delete_value(Py_tss_t *key)
     PyAPI_FUNC(void) PyThread_ReInitTSS(void)
 
-The specification also adds three new features:
+The specification also adds a few new features:
 
 * A new type ``Py_tss_t``--an opaque type the definition of which may
   depend on the underlying TLS implementation.  It is defined::
@@ -73,12 +73,18 @@ The specification also adds three new features:
 * A constant default value for ``Py_tss_t`` variables,
   ``Py_tss_NEEDS_INIT``.
 
-* A new inline function::
+* Three new functions::
 
-      static inline bool PyThread_tss_is_created(Py_tss_t key)
+      PyAPI_FUNC(Py_tss_t *) PyThread_tss_alloc(void)
+      PyAPI_FUNC(void) PyThread_tss_free(Py_tss_t *key)
+      PyAPI_FUNC(bool) PyThread_tss_is_created(Py_tss_t *key)
 
-  which returns ``true`` if the given ``Py_tss_t`` has been initialized
-  (i.e. by ``PyThread_tss_create``).
+  The first two are needed for dynamic (de-)allocation of a `Py_tss_t`,
+  particularly in extension modules built with `Py_LIMITED_API`, where
+  static allocation of this type is not possible due to its implementation
+  being opaque at build time. ``PyThread_tss_is_created`` returns ``true``
+  if the given ``Py_tss_t`` has been initialized (i.e. by
+  ``PyThread_tss_create``).
 
 The new ``PyThread_tss_`` functions are almost exactly analogous to their
 original counterparts with a minor difference:  Whereas
@@ -90,8 +96,11 @@ by ``Py_tss_NEEDS_INIT``. The returned status status code is zero on success
 and non-zero on failure.  The meanings of non-zero status codes are not
 otherwise defined by this specification.
 
-Similarly ``PyThread_tss_delete`` is passed a ``Py_tss_t*`` whereas
-previouly the key was passed to ``PyThread_delete_key`` by value.
+Similarly the other ``PyThread_tss_`` functions are passed a ``Py_tss_t*``
+whereas previously the key was passed by value.  This change is necessary, as
+being an opaque type, the ``Py_tss_t`` type could hypothetically be almost
+any size.  This is especially necessary for extension modules built with
+``Py_LIMITED_API``, where the size of the type is not known.
 
 The old ``PyThread_*_key*`` functions will be marked as deprecated in the
 documentation, but will not generate runtime deprecation warnings.
@@ -112,18 +121,18 @@ With the proposed changes, a TSS key is initialized like::
 
 The initialization state of the key can then be checked like::
 
-    assert(PyThread_tss_is_created(tss_key));
+    assert(PyThread_tss_is_created(&tss_key));
 
 The rest of the API is used analogously to the old API::
 
     int the_value = 1;
-    if (PyThread_tss_get(tss_key) == NULL) {
-        PyThread_tss_set(tss_key, (void *)&the_value);
-        assert(PyThread_tss_get(tss_key) != NULL);
+    if (PyThread_tss_get(&tss_key) == NULL) {
+        PyThread_tss_set(&tss_key, (void *)&the_value);
+        assert(PyThread_tss_get(&tss_key) != NULL);
     }
     /* ... once done with the key ... */
     PyThread_tss_delete(&tss_key);
-    assert(!PyThread_tss_is_created(tss_key));
+    assert(!PyThread_tss_is_created(&tss_key));
 
 
 Motivation