diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index f01e5884c6f..90d288f7393 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -93,11 +93,6 @@ typedef struct {
     PyObject *sw_arg;
 } TaskStepMethWrapper;
 
-typedef struct {
-    PyObject_HEAD
-    TaskObj *ww_task;
-} TaskWakeupMethWrapper;
-
 typedef struct {
     PyObject_HEAD
     PyObject *rl_loop;
@@ -1870,93 +1865,15 @@ TaskStepMethWrapper_new(TaskObj *task, PyObject *arg)
     return (PyObject*) o;
 }
 
-/* ----- Task._wakeup wrapper */
+/* ----- Task._wakeup implementation */
 
-static PyObject *
-TaskWakeupMethWrapper_call(TaskWakeupMethWrapper *o,
-                           PyObject *args, PyObject *kwds)
-{
-    PyObject *fut;
-
-    if (kwds != NULL && PyDict_GET_SIZE(kwds) != 0) {
-        PyErr_SetString(PyExc_TypeError, "function takes no keyword arguments");
-        return NULL;
-    }
-    if (!PyArg_ParseTuple(args, "O", &fut)) {
-        return NULL;
-    }
-
-    return task_wakeup(o->ww_task, fut);
-}
-
-static int
-TaskWakeupMethWrapper_clear(TaskWakeupMethWrapper *o)
-{
-    Py_CLEAR(o->ww_task);
-    return 0;
-}
-
-static int
-TaskWakeupMethWrapper_traverse(TaskWakeupMethWrapper *o,
-                               visitproc visit, void *arg)
-{
-    Py_VISIT(o->ww_task);
-    return 0;
-}
-
-static void
-TaskWakeupMethWrapper_dealloc(TaskWakeupMethWrapper *o)
-{
-    PyObject_GC_UnTrack(o);
-    (void)TaskWakeupMethWrapper_clear(o);
-    Py_TYPE(o)->tp_free(o);
-}
-
-static PyObject *
-TaskWakeupMethWrapper_get___self__(TaskWakeupMethWrapper *o, void *Py_UNUSED(ignored))
-{
-    if (o->ww_task) {
-        Py_INCREF(o->ww_task);
-        return (PyObject*)o->ww_task;
-    }
-    Py_RETURN_NONE;
-}
-
-static PyGetSetDef TaskWakeupMethWrapper_getsetlist[] = {
-    {"__self__", (getter)TaskWakeupMethWrapper_get___self__, NULL, NULL},
-    {NULL} /* Sentinel */
+static  PyMethodDef TaskWakeupDef = {
+    "task_wakeup",
+    (PyCFunction)task_wakeup,
+    METH_O,
+    NULL
 };
 
-static PyTypeObject TaskWakeupMethWrapper_Type = {
-    PyVarObject_HEAD_INIT(NULL, 0)
-    "TaskWakeupMethWrapper",
-    .tp_basicsize = sizeof(TaskWakeupMethWrapper),
-    .tp_itemsize = 0,
-    .tp_dealloc = (destructor)TaskWakeupMethWrapper_dealloc,
-    .tp_call = (ternaryfunc)TaskWakeupMethWrapper_call,
-    .tp_getattro = PyObject_GenericGetAttr,
-    .tp_flags = Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,
-    .tp_traverse = (traverseproc)TaskWakeupMethWrapper_traverse,
-    .tp_clear = (inquiry)TaskWakeupMethWrapper_clear,
-    .tp_getset = TaskWakeupMethWrapper_getsetlist,
-};
-
-static PyObject *
-TaskWakeupMethWrapper_new(TaskObj *task)
-{
-    TaskWakeupMethWrapper *o;
-    o = PyObject_GC_New(TaskWakeupMethWrapper, &TaskWakeupMethWrapper_Type);
-    if (o == NULL) {
-        return NULL;
-    }
-
-    Py_INCREF(task);
-    o->ww_task = task;
-
-    PyObject_GC_Track(o);
-    return (PyObject*) o;
-}
-
 /* ----- Task introspection helpers */
 
 static int
@@ -2803,7 +2720,7 @@ task_step_impl(TaskObj *task, PyObject *exc)
         fut->fut_blocking = 0;
 
         /* result.add_done_callback(task._wakeup) */
-        wrapper = TaskWakeupMethWrapper_new(task);
+        wrapper = PyCFunction_New(&TaskWakeupDef, (PyObject *)task);
         if (wrapper == NULL) {
             goto fail;
         }
@@ -2884,7 +2801,7 @@ task_step_impl(TaskObj *task, PyObject *exc)
             goto fail;
         }
 
-        wrapper = TaskWakeupMethWrapper_new(task);
+        wrapper = PyCFunction_New(&TaskWakeupDef, (PyObject *)task);
         if (wrapper == NULL) {
             goto fail;
         }
@@ -3458,9 +3375,6 @@ PyInit__asyncio(void)
     if (PyType_Ready(&TaskStepMethWrapper_Type) < 0) {
         return NULL;
     }
-    if (PyType_Ready(&TaskWakeupMethWrapper_Type) < 0) {
-        return NULL;
-    }
     if (PyType_Ready(&PyRunningLoopHolder_Type) < 0) {
         return NULL;
     }