diff --git a/Lib/test/test_sys_settrace.py b/Lib/test/test_sys_settrace.py
--- a/Lib/test/test_sys_settrace.py
+++ b/Lib/test/test_sys_settrace.py
@@ -238,6 +238,14 @@
         self.events = []
     def trace(self, frame, event, arg):
         self.events.append((frame.f_lineno, event))
+        if event == 'call':
+            if ('call_stop_tracing' in frame.f_locals and
+                    frame.f_locals['call_stop_tracing'] is True):
+                return
+        elif event == 'line':
+            if ('line_stop_tracing' in frame.f_locals and
+                    frame.f_locals['line_stop_tracing'] is True):
+                return
         return self.trace
     def traceWithGenexp(self, frame, event, arg):
         (o for o in [1])
@@ -388,6 +396,60 @@
              (257, 'line'),
              (257, 'return')])
 
+    def test_17_line_stop_tracing(self):
+        # issue 11992: tracing not disabled when the local trace function
+        # returns None.
+        def func():
+            line_stop_tracing = True
+            lineno = 2
+            lineno = 3
+
+        func.events = [(0, 'call'),
+                       (1, 'line'),
+                       (2, 'line')]
+
+        self.run_test(func)
+
+    def test_18_call_stop_tracing(self):
+        # issue 20040: tracing not disabled in generator when the system trace
+        # function returns None.
+        def func():
+            it = gen()
+            next(it)
+            next(it)
+            sys.settrace(None)
+
+        def gen():
+            lineno = 7
+            call_stop_tracing = True
+            yield call_stop_tracing
+            yield call_stop_tracing
+
+        func.events = [(0, 'call'),
+                        (1, 'line'),
+                        (2, 'line'),
+                        (6, 'call'),
+                        (7, 'line'),
+                        (8, 'line'),
+                        (9, 'line'),
+                        (9, 'return'),
+                        (3, 'line'),
+                        (9, 'call'),
+                        (4, 'line')]
+
+        self.run_test(func)
+
+    def test_19_none_f_trace(self):
+        # issue 20041: TypeError when f_trace is None.
+        def func():
+            sys._getframe().f_trace = None
+            lineno = 2
+
+        func.events = [(0, 'call'),
+                       (1, 'line')]
+
+        self.run_test(func)
+
 
 class RaisingTraceFuncTestCase(unittest.TestCase):
     def setUp(self):