diff --git a/Lib/asyncio/tasks.py b/Lib/asyncio/tasks.py
index 38c23851102a8b..059143fb9086fb 100644
--- a/Lib/asyncio/tasks.py
+++ b/Lib/asyncio/tasks.py
@@ -205,8 +205,11 @@ def cancel(self, msg=None):
         if self.done():
             return False
         self._num_cancels_requested += 1
-        if self._num_cancels_requested > 1:
-            return False
+        # These two lines are controversial.  See discussion starting at
+        # https://github.com/python/cpython/pull/31394#issuecomment-1053545331
+        # Also remember that this is duplicated in _asynciomodule.c.
+        # if self._num_cancels_requested > 1:
+        #     return False
         if self._fut_waiter is not None:
             if self._fut_waiter.cancel(msg=msg):
                 # Leave self._fut_waiter; it may be a Task that
diff --git a/Lib/test/test_asyncio/test_tasks.py b/Lib/test/test_asyncio/test_tasks.py
index b30f8f56dfa726..950879204e703b 100644
--- a/Lib/test/test_asyncio/test_tasks.py
+++ b/Lib/test/test_asyncio/test_tasks.py
@@ -514,7 +514,11 @@ async def task():
             self.assertTrue(t.cancel())
             self.assertTrue(t.cancelling())
             self.assertIn(" cancelling ", repr(t))
-            self.assertFalse(t.cancel())
+
+            # Since we commented out two lines from Task.cancel(),
+            # this t.cancel() call now returns True.
+            # self.assertFalse(t.cancel())
+            self.assertTrue(t.cancel())
 
             with self.assertRaises(asyncio.CancelledError):
                 loop.run_until_complete(t)
diff --git a/Modules/_asynciomodule.c b/Modules/_asynciomodule.c
index 88471239529a55..2a6c0b335ccfb0 100644
--- a/Modules/_asynciomodule.c
+++ b/Modules/_asynciomodule.c
@@ -2206,9 +2206,13 @@ _asyncio_Task_cancel_impl(TaskObj *self, PyObject *msg)
     }
 
     self->task_num_cancels_requested += 1;
-    if (self->task_num_cancels_requested > 1) {
-        Py_RETURN_FALSE;
-    }
+
+    // These three lines are controversial.  See discussion starting at
+    // https://github.com/python/cpython/pull/31394#issuecomment-1053545331
+    // and corresponding code in tasks.py.
+    // if (self->task_num_cancels_requested > 1) {
+    //     Py_RETURN_FALSE;
+    // }
 
     if (self->task_fut_waiter) {
         PyObject *res;