diff --git a/Doc/library/timeit.rst b/Doc/library/timeit.rst
index ef7a4e40be6590..26a9b4ffde4ff3 100644
--- a/Doc/library/timeit.rst
+++ b/Doc/library/timeit.rst
@@ -94,7 +94,7 @@ The module defines three convenience functions and a public class:
       :func:`time.perf_counter` is now the default timer.
 
 
-.. class:: Timer(stmt='pass', setup='pass', timer=<timer function>, globals=None)
+.. class:: Timer(stmt='pass', setup='pass', timer=<timer function>, globals=None, target_time=0.2)
 
    Class for timing execution speed of small code snippets.
 
@@ -119,6 +119,8 @@ The module defines three convenience functions and a public class:
 
    .. versionchanged:: 3.5
       The optional *globals* parameter was added.
+   .. versionchanged:: 3.8
+      The optional *target_time* parameter was added.
 
    .. method:: Timer.timeit(number=1000000)
 
@@ -141,20 +143,22 @@ The module defines three convenience functions and a public class:
             timeit.Timer('for i in range(10): oct(i)', 'gc.enable()').timeit()
 
 
-   .. method:: Timer.autorange(callback=None)
+   .. method:: Timer.autorange(callback=None, target_time=0.2)
 
       Automatically determine how many times to call :meth:`.timeit`.
 
       This is a convenience function that calls :meth:`.timeit` repeatedly
-      so that the total time >= 0.2 second, returning the eventual
+      so that the total time is greater than or equal to *target_time*, returning the eventual
       (number of loops, time taken for that number of loops). It calls
       :meth:`.timeit` with increasing numbers from the sequence 1, 2, 5,
-      10, 20, 50, ... until the time taken is at least 0.2 second.
+      10, 20, 50, ... until the time taken is at least *target_time*.
 
       If *callback* is given and is not ``None``, it will be called after
       each trial with two arguments: ``callback(number, time_taken)``.
 
       .. versionadded:: 3.6
+      .. versionchanged:: 3.8
+         The optional *target_time* parameter was added.
 
 
    .. method:: Timer.repeat(repeat=5, number=1000000)
diff --git a/Lib/test/test_timeit.py b/Lib/test/test_timeit.py
index e02d4a71a9ba7c..65992fd6f70e6a 100644
--- a/Lib/test/test_timeit.py
+++ b/Lib/test/test_timeit.py
@@ -10,6 +10,9 @@
 # timeit's default number of iterations.
 DEFAULT_NUMBER = 1000000
 
+# timeit's default target time.
+DEFAULT_TARGET_TIME = 0.2
+
 # timeit's default number of repetitions.
 DEFAULT_REPEAT = 5
 
@@ -107,8 +110,8 @@ def timeit(self, stmt, setup, number=None, globals=None):
             kwargs['number'] = number
         delta_time = t.timeit(**kwargs)
         self.assertEqual(self.fake_timer.setup_calls, 1)
-        self.assertEqual(self.fake_timer.count, number)
-        self.assertEqual(delta_time, number)
+        self.assertEqual(self.fake_timer.count, number if number else 1)
+        self.assertEqual(delta_time, number if number else (1, 1.0))
 
     # Takes too long to run in debug build.
     #def test_timeit_default_iters(self):
@@ -139,7 +142,7 @@ def test_timeit_callable_stmt_and_setup(self):
     def test_timeit_function_zero_iters(self):
         delta_time = timeit.timeit(self.fake_stmt, self.fake_setup, number=0,
                 timer=FakeTimer())
-        self.assertEqual(delta_time, 0)
+        self.assertEqual(delta_time, (1, 1.0))
 
     def test_timeit_globals_args(self):
         global _global_timer
@@ -165,9 +168,13 @@ def repeat(self, stmt, setup, repeat=None, number=None):
         else:
             kwargs['number'] = number
         delta_times = t.repeat(**kwargs)
-        self.assertEqual(self.fake_timer.setup_calls, repeat)
-        self.assertEqual(self.fake_timer.count, repeat * number)
-        self.assertEqual(delta_times, repeat * [float(number)])
+        self.assertEqual(self.fake_timer.setup_calls, repeat if number > 0
+                else 1)
+        # self.assertEqual(self.fake_timer.setup_calls, )
+        self.assertEqual(self.fake_timer.count,
+                         (repeat * number) if number else 1)
+        self.assertEqual(delta_times,
+                         repeat * [float(number)] if number else (1, 1.0))
 
     # Takes too long to run in debug build.
     #def test_repeat_default(self):
@@ -179,6 +186,9 @@ def test_repeat_zero_reps(self):
     def test_repeat_zero_iters(self):
         self.repeat(self.fake_stmt, self.fake_setup, number=0)
 
+    def test_repeat_with_iters(self):
+        self.repeat(self.fake_stmt, self.fake_setup, number=1)
+
     def test_repeat_few_reps_and_iters(self):
         self.repeat(self.fake_stmt, self.fake_setup, repeat=3, number=5)
 
@@ -208,7 +218,12 @@ def test_repeat_function_zero_reps(self):
     def test_repeat_function_zero_iters(self):
         delta_times = timeit.repeat(self.fake_stmt, self.fake_setup, number=0,
                 timer=FakeTimer())
-        self.assertEqual(delta_times, DEFAULT_REPEAT * [0.0])
+        self.assertEqual(delta_times, (1, 1.0))
+
+    def test_repeat_function_with_iters(self):
+        delta_times = timeit.repeat(self.fake_stmt, self.fake_setup, number=1,
+                                    timer=FakeTimer())
+        self.assertEqual(delta_times, [1.0, 1.0, 1.0, 1.0, 1.0])
 
     def assert_exc_string(self, exc_string, expected_exc_name):
         exc_lines = exc_string.splitlines()
@@ -354,38 +369,66 @@ def test_main_exception_fixed_reps(self):
             s = self.run_main(switches=['-n1', '1/0'])
         self.assert_exc_string(error_stringio.getvalue(), 'ZeroDivisionError')
 
-    def autorange(self, seconds_per_increment=1/1024, callback=None):
+    def autorange(self, seconds_per_increment=1/1024, callback=None,
+                  target_time=0.2):
         timer = FakeTimer(seconds_per_increment=seconds_per_increment)
         t = timeit.Timer(stmt=self.fake_stmt, setup=self.fake_setup, timer=timer)
-        return t.autorange(callback)
+        return t.autorange(callback, target_time)
+
+    def autorange_with_callback(self, loop_count, expected_output,
+                                target_time=0.2):
+        def callback(a, b):
+            print("{} {:.3f}".format(a, b))
+        with captured_stdout() as s:
+            num_loops, time_taken = self.autorange(callback=callback,
+                                                   target_time=target_time)
+            self.assertEqual(num_loops, loop_count)
+            self.assertEqual(time_taken, loop_count/1024)
+            self.assertEqual(s.getvalue(), expected_output)
 
     def test_autorange(self):
         num_loops, time_taken = self.autorange()
         self.assertEqual(num_loops, 500)
         self.assertEqual(time_taken, 500/1024)
 
+    def test_autorange_with_target_time(self):
+        num_loops, time_taken = self.autorange(target_time=0.6)
+        self.assertEqual(num_loops, 1000)
+        self.assertEqual(time_taken, 1000/1024)
+
     def test_autorange_second(self):
         num_loops, time_taken = self.autorange(seconds_per_increment=1.0)
         self.assertEqual(num_loops, 1)
         self.assertEqual(time_taken, 1.0)
 
     def test_autorange_with_callback(self):
-        def callback(a, b):
-            print("{} {:.3f}".format(a, b))
-        with captured_stdout() as s:
-            num_loops, time_taken = self.autorange(callback=callback)
-        self.assertEqual(num_loops, 500)
-        self.assertEqual(time_taken, 500/1024)
-        expected = ('1 0.001\n'
-                    '2 0.002\n'
-                    '5 0.005\n'
-                    '10 0.010\n'
-                    '20 0.020\n'
-                    '50 0.049\n'
-                    '100 0.098\n'
-                    '200 0.195\n'
-                    '500 0.488\n')
-        self.assertEqual(s.getvalue(), expected)
+        expected = dedent('''\
+                    1 0.001
+                    2 0.002
+                    5 0.005
+                    10 0.010
+                    20 0.020
+                    50 0.049
+                    100 0.098
+                    200 0.195
+                    500 0.488
+        ''')
+        self.autorange_with_callback(500, expected)
+
+    def test_autorange_with_callback_and_target_time(self):
+        expected = dedent('''\
+                    1 0.001
+                    2 0.002
+                    5 0.005
+                    10 0.010
+                    20 0.020
+                    50 0.049
+                    100 0.098
+                    200 0.195
+                    500 0.488
+                    1000 0.977
+        ''')
+        self.autorange_with_callback(1000, expected, target_time=0.6)
 
 
 if __name__ == '__main__':
diff --git a/Lib/timeit.py b/Lib/timeit.py
index c0362bcc5f3e24..955f0c3a9bf62c 100755
--- a/Lib/timeit.py
+++ b/Lib/timeit.py
@@ -59,6 +59,7 @@
 default_number = 1000000
 default_repeat = 5
 default_timer = time.perf_counter
+default_target_time = 0.2
 
 _globals = globals
 
@@ -98,9 +99,10 @@ class Timer:
     """
 
     def __init__(self, stmt="pass", setup="pass", timer=default_timer,
-                 globals=None):
+                 globals=None, target_time=default_target_time):
         """Constructor.  See class doc string."""
         self.timer = timer
+        self.target_time = target_time
         local_ns = {}
         global_ns = _globals() if globals is None else globals
         init = ''
@@ -169,6 +171,8 @@ def timeit(self, number=default_number):
         to one million.  The main statement, the setup statement and
         the timer function to be used are passed to the constructor.
         """
+        if number == 0 or number is None:
+            return self.autorange(target_time=self.target_time)
         it = itertools.repeat(None, number)
         gcold = gc.isenabled()
         gc.disable()
@@ -199,14 +203,17 @@ def repeat(self, repeat=default_repeat, number=default_number):
         interested in.  After that, you should look at the entire
         vector and apply common sense rather than statistics.
         """
+        if number == 0 or number is None:
+            return self.autorange(target_time=self.target_time)
         r = []
         for i in range(repeat):
             t = self.timeit(number)
             r.append(t)
         return r
 
-    def autorange(self, callback=None):
-        """Return the number of loops and time taken so that total time >= 0.2.
+    def autorange(self, callback=None, target_time=None):
+        """Return the number of loops and time taken so that total time
+        is greater than or equal to *target_time*.
 
         Calls the timeit method with increasing numbers from the sequence
         1, 2, 5, 10, 20, 50, ... until the time taken is at least 0.2
@@ -215,6 +222,8 @@ def autorange(self, callback=None):
         If *callback* is given and is not None, it will be called after
         each trial with two arguments: ``callback(number, time_taken)``.
         """
+        if target_time is None:
+            target_time = self.target_time
         i = 1
         while True:
             for j in 1, 2, 5:
@@ -222,7 +231,7 @@ def autorange(self, callback=None):
                 time_taken = self.timeit(number)
                 if callback:
                     callback(number, time_taken)
-                if time_taken >= 0.2:
+                if time_taken >= target_time:
                     return (number, time_taken)
             i *= 10
 
diff --git a/Misc/ACKS b/Misc/ACKS
index 06e288dfcb2f18..6fea3a5f1e4471 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -55,6 +55,7 @@ Juancarlo Añez
 Chris Angelico
 Jérémy Anger
 Jon Anglin
+Michele Angrisano
 Ankur Ankan
 Heidi Annexstad
 Ramchandra Apte
diff --git a/Misc/NEWS.d/next/Library/2019-04-25-19-15-11.bpo-36461.BRX4xA.rst b/Misc/NEWS.d/next/Library/2019-04-25-19-15-11.bpo-36461.BRX4xA.rst
new file mode 100644
index 00000000000000..9b738f77d8aca3
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-04-25-19-15-11.bpo-36461.BRX4xA.rst
@@ -0,0 +1,2 @@
+A new parameter *total_time* was added to the ``timeit.autorange()``
+function.