diff --git a/Doc/library/datetime.rst b/Doc/library/datetime.rst
index fb41aee..c935e35 100644
--- a/Doc/library/datetime.rst
+++ b/Doc/library/datetime.rst
@@ -2093,7 +2093,7 @@
 |           | where 0 is Sunday and 6 is     |                        |       |
 |           | Saturday.                      |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%d``    | Day of the month as a          | 01, 02, ..., 31        |       |
+| ``%d``    | Day of the month as a          | 01, 02, ..., 31        | \(9)  |
 |           | zero-padded decimal number.    |                        |       |
 +-----------+--------------------------------+------------------------+-------+
 | ``%b``    | Month as locale's abbreviated  || Jan, Feb, ..., Dec    | \(1)  |
@@ -2106,29 +2106,29 @@
 |           |                                || Januar, Februar, ..., |       |
 |           |                                |  Dezember (de_DE)      |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%m``    | Month as a zero-padded         | 01, 02, ..., 12        |       |
+| ``%m``    | Month as a zero-padded         | 01, 02, ..., 12        | \(9)  |
 |           | decimal number.                |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%y``    | Year without century as a      | 00, 01, ..., 99        |       |
+| ``%y``    | Year without century as a      | 00, 01, ..., 99        | \(9)  |
 |           | zero-padded decimal number.    |                        |       |
 +-----------+--------------------------------+------------------------+-------+
 | ``%Y``    | Year with century as a decimal | 0001, 0002, ..., 2013, | \(2)  |
 |           | number.                        | 2014, ..., 9998, 9999  |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%H``    | Hour (24-hour clock) as a      | 00, 01, ..., 23        |       |
+| ``%H``    | Hour (24-hour clock) as a      | 00, 01, ..., 23        | \(9)  |
 |           | zero-padded decimal number.    |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%I``    | Hour (12-hour clock) as a      | 01, 02, ..., 12        |       |
+| ``%I``    | Hour (12-hour clock) as a      | 01, 02, ..., 12        | \(9)  |
 |           | zero-padded decimal number.    |                        |       |
 +-----------+--------------------------------+------------------------+-------+
 | ``%p``    | Locale's equivalent of either  || AM, PM (en_US);       | \(1), |
 |           | AM or PM.                      || am, pm (de_DE)        | \(3)  |
 +-----------+--------------------------------+------------------------+-------+
-| ``%M``    | Minute as a zero-padded        | 00, 01, ..., 59        |       |
+| ``%M``    | Minute as a zero-padded        | 00, 01, ..., 59        | \(9)  |
 |           | decimal number.                |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%S``    | Second as a zero-padded        | 00, 01, ..., 59        | \(4)  |
-|           | decimal number.                |                        |       |
+| ``%S``    | Second as a zero-padded        | 00, 01, ..., 59        | \(4), |
+|           | decimal number.                |                        | \(9)  |
 +-----------+--------------------------------+------------------------+-------+
 | ``%f``    | Microsecond as a decimal       | 000000, 000001, ...,   | \(5)  |
 |           | number, zero-padded on the     | 999999                 |       |
@@ -2142,19 +2142,19 @@
 | ``%Z``    | Time zone name (empty string   | (empty), UTC, EST, CST |       |
 |           | if the object is naive).       |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%j``    | Day of the year as a           | 001, 002, ..., 366     |       |
+| ``%j``    | Day of the year as a           | 001, 002, ..., 366     | \(9)  |
 |           | zero-padded decimal number.    |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%U``    | Week number of the year        | 00, 01, ..., 53        | \(7)  |
-|           | (Sunday as the first day of    |                        |       |
+| ``%U``    | Week number of the year        | 00, 01, ..., 53        | \(7), |
+|           | (Sunday as the first day of    |                        | \(9)  |
 |           | the week) as a zero padded     |                        |       |
 |           | decimal number. All days in a  |                        |       |
 |           | new year preceding the first   |                        |       |
 |           | Sunday are considered to be in |                        |       |
 |           | week 0.                        |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%W``    | Week number of the year        | 00, 01, ..., 53        | \(7)  |
-|           | (Monday as the first day of    |                        |       |
+| ``%W``    | Week number of the year        | 00, 01, ..., 53        | \(7), |
+|           | (Monday as the first day of    |                        | \(9)  |
 |           | the week) as a decimal number. |                        |       |
 |           | All days in a new year         |                        |       |
 |           | preceding the first Monday     |                        |       |
@@ -2194,8 +2194,8 @@
 | ``%u``    | ISO 8601 weekday as a decimal  | 1, 2, ..., 7           |       |
 |           | number where 1 is Monday.      |                        |       |
 +-----------+--------------------------------+------------------------+-------+
-| ``%V``    | ISO 8601 week as a decimal     | 01, 02, ..., 53        | \(8)  |
-|           | number with Monday as          |                        |       |
+| ``%V``    | ISO 8601 week as a decimal     | 01, 02, ..., 53        | \(8), |
+|           | number with Monday as          |                        | \(9)  |
 |           | the first day of the week.     |                        |       |
 |           | Week 01 is the week containing |                        |       |
 |           | Jan 4.                         |                        |       |
@@ -2291,6 +2291,11 @@
    :meth:`strptime` format string. Also note that ``%G`` and ``%Y`` are not
    interchangeable.
 
+(9)
+   When used with the :meth:`strptime` method, the leading zero is optional
+   for  formats ``%d``, ``%m``, ``%H``, ``%I``, ``%M``, ``%S``, ``%J``, ``%U``,
+   ``%W``, and ``%V``. Format ``%y`` does require a leading zero.
+
 .. rubric:: Footnotes
 
 .. [#] If, that is, we ignore the effects of Relativity
diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index 239a0b5..53de065 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -2501,6 +2501,7 @@
                 self.assertEqual(expected, got)
 
         strptime = self.theclass.strptime
+
         self.assertEqual(strptime("+0002", "%z").utcoffset(), 2 * MINUTE)
         self.assertEqual(strptime("-0002", "%z").utcoffset(), -2 * MINUTE)
         self.assertEqual(
@@ -2535,6 +2536,40 @@
         with self.assertRaises(ValueError): strptime("-2400", "%z")
         with self.assertRaises(ValueError): strptime("-000", "%z")
 
+    def test_strptime_single_digit(self):
+        # bpo-34903: Check that single digit dates and times are allowed.
+
+        strptime = self.theclass.strptime
+
+        with self.assertRaises(ValueError):
+            # %y does require two digits.
+            newdate = strptime('01/02/3 04:05:06', '%d/%m/%y %H:%M:%S')
+        dt1 = self.theclass(2003, 2, 1, 4, 5, 6)
+        dt2 = self.theclass(2003, 1, 2, 4, 5, 6)
+        dt3 = self.theclass(2003, 2, 1, 0, 0, 0)
+        dt4 = self.theclass(2003, 1, 25, 0, 0, 0)
+        inputs = [
+            ('%d', '1/02/03 4:5:6', '%d/%m/%y %H:%M:%S', dt1),
+            ('%m', '01/2/03 4:5:6', '%d/%m/%y %H:%M:%S', dt1),
+            ('%H', '01/02/03 4:05:06', '%d/%m/%y %H:%M:%S', dt1),
+            ('%M', '01/02/03 04:5:06', '%d/%m/%y %H:%M:%S', dt1),
+            ('%S', '01/02/03 04:05:6', '%d/%m/%y %H:%M:%S', dt1),
+            ('%j', '2/03 04am:05:06', '%j/%y %I%p:%M:%S',dt2),
+            ('%I', '02/03 4am:05:06', '%j/%y %I%p:%M:%S',dt2),
+            ('%w', '6/04/03', '%w/%U/%y', dt3),
+            # %u requires a single digit.
+            ('%W', '6/4/2003', '%u/%W/%Y', dt3),
+            ('%V', '6/4/2003', '%u/%V/%G', dt4),
+        ]
+        for reason, string, format, target in inputs:
+            reason = 'test single digit ' + reason
+            with self.subTest(reason=reason,
+                              string=string,
+                              format=format,
+                              target=target):
+                newdate = strptime(string, format)
+                self.assertEqual(newdate, target, msg=reason)
+
     def test_more_timetuple(self):
         # This tests fields beyond those tested by the TestDate.test_timetuple.
         t = self.theclass(2004, 12, 31, 6, 22, 33)
diff --git a/Misc/NEWS.d/next/Documentation/2019-06-17-09-36-46.bpo-34903.r_wGRc.rst b/Misc/NEWS.d/next/Documentation/2019-06-17-09-36-46.bpo-34903.r_wGRc.rst
new file mode 100644
index 0000000..7e277f4
--- /dev/null
+++ b/Misc/NEWS.d/next/Documentation/2019-06-17-09-36-46.bpo-34903.r_wGRc.rst
@@ -0,0 +1 @@
+Documented that in :meth:`datetime.datetime.strptime()`, the leading zero in some two-digit formats is optional. Patch by Mike Gleen.