diff --git a/Lib/test/test_time.py b/Lib/test/test_time.py
index 303918960b6..42799b2a21c 100644
--- a/Lib/test/test_time.py
+++ b/Lib/test/test_time.py
@@ -470,8 +470,9 @@ class TimeTestCase(unittest.TestCase):
         t2 = time.monotonic()
         dt = t2 - t1
         self.assertGreater(t2, t1)
-        # Issue #20101: On some Windows machines, dt may be slightly low
-        self.assertTrue(0.45 <= dt <= 1.0, dt)
+        # bpo-20101: tolerate a difference of 50 ms because of bad timer
+        # resolution on Windows
+        self.assertTrue(0.450 <= dt)
 
         # monotonic() is a monotonic but non adjustable clock
         info = time.get_clock_info('monotonic')
diff --git a/Misc/NEWS.d/next/Tests/2019-04-23-17-48-11.bpo-36454.0q4lQz.rst b/Misc/NEWS.d/next/Tests/2019-04-23-17-48-11.bpo-36454.0q4lQz.rst
new file mode 100644
index 00000000000..151c7ab0404
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2019-04-23-17-48-11.bpo-36454.0q4lQz.rst
@@ -0,0 +1,3 @@
+Change test_time.test_monotonic() to test only the lower bound of elapsed time
+after a sleep command rather than the upper bound. This prevents unnecessary
+test failures on slow buildbots. Patch by Victor Stinner.