diff --git a/Doc/library/calendar.rst b/Doc/library/calendar.rst
index a415b4792a6..8fe93fd4de3 100644
--- a/Doc/library/calendar.rst
+++ b/Doc/library/calendar.rst
@@ -53,17 +53,40 @@ it's the base calendar for all computations.
       month that are required to get a complete week.
 
 
-   .. method:: itermonthdays2(year, month)
-
-      Return an iterator for the month *month* in the year *year* similar to
-      :meth:`itermonthdates`. Days returned will be tuples consisting of a day
-      number and a week day number.
-
-
    .. method:: itermonthdays(year, month)
 
       Return an iterator for the month *month* in the year *year* similar to
-      :meth:`itermonthdates`. Days returned will simply be day numbers.
+      :meth:`itermonthdates`, but not restricted by the :class:`datetime.date`
+      range. Days returned will simply be day of the month numbers.  For the
+      days outside of the specified month, the day number is ``0``.
+
+
+   .. method:: itermonthdays2(year, month)
+
+      Return an iterator for the month *month* in the year *year* similar to
+      :meth:`itermonthdates`, but not restricted by the :class:`datetime.date`
+      range. Days returned will be tuples consisting of a day of the month
+      number and a week day number.
+
+
+   .. method:: itermonthdays3(year, month)
+
+      Return an iterator for the month *month* in the year *year* similar to
+      :meth:`itermonthdates`, but not restricted by the :class:`datetime.date`
+      range. Days returned will be tuples consisting of a year, a month and a day
+      of the month numbers.
+
+      .. versionadded:: 3.7
+
+
+   .. method:: itermonthdays4(year, month)
+
+      Return an iterator for the month *month* in the year *year* similar to
+      :meth:`itermonthdates`, but not restricted by the :class:`datetime.date`
+      range. Days returned will be tuples consisting of a year, a month, a day
+      of the month, and a day of the week numbers.
+
+      .. versionadded:: 3.7
 
 
    .. method:: monthdatescalendar(year, month)
diff --git a/Lib/calendar.py b/Lib/calendar.py
index 0218e2d3977..fb594e0f5b0 100644
--- a/Lib/calendar.py
+++ b/Lib/calendar.py
@@ -126,6 +126,24 @@ def monthrange(year, month):
     return day1, ndays
 
 
+def monthlen(year, month):
+    return mdays[month] + (month == February and isleap(year))
+
+
+def prevmonth(year, month):
+    if month == 1:
+        return year-1, 12
+    else:
+        return year, month-1
+
+
+def nextmonth(year, month):
+    if month == 12:
+        return year+1, 1
+    else:
+        return year, month+1
+
+
 class Calendar(object):
     """
     Base calendar class. This class doesn't do any formatting. It simply
@@ -157,28 +175,8 @@ class Calendar(object):
         values and will always iterate through complete weeks, so it will yield
         dates outside the specified month.
         """
-        date = datetime.date(year, month, 1)
-        # Go back to the beginning of the week
-        days = (date.weekday() - self.firstweekday) % 7
-        date -= datetime.timedelta(days=days)
-        oneday = datetime.timedelta(days=1)
-        while True:
-            yield date
-            try:
-                date += oneday
-            except OverflowError:
-                # Adding one day could fail after datetime.MAXYEAR
-                break
-            if date.month != month and date.weekday() == self.firstweekday:
-                break
-
-    def itermonthdays2(self, year, month):
-        """
-        Like itermonthdates(), but will yield (day number, weekday number)
-        tuples. For days outside the specified month the day number is 0.
-        """
-        for i, d in enumerate(self.itermonthdays(year, month), self.firstweekday):
-            yield d, i % 7
+        for y, m, d in self.itermonthdays3(year, month):
+            yield datetime.date(y, m, d)
 
     def itermonthdays(self, year, month):
         """
@@ -192,6 +190,40 @@ class Calendar(object):
         days_after = (self.firstweekday - day1 - ndays) % 7
         yield from repeat(0, days_after)
 
+    def itermonthdays2(self, year, month):
+        """
+        Like itermonthdates(), but will yield (day number, weekday number)
+        tuples. For days outside the specified month the day number is 0.
+        """
+        for i, d in enumerate(self.itermonthdays(year, month), self.firstweekday):
+            yield d, i % 7
+
+    def itermonthdays3(self, year, month):
+        """
+        Like itermonthdates(), but will yield (year, month, day) tuples.  Can be
+        used for dates outside of datetime.date range.
+        """
+        day1, ndays = monthrange(year, month)
+        days_before = (day1 - self.firstweekday) % 7
+        days_after = (self.firstweekday - day1 - ndays) % 7
+        y, m = prevmonth(year, month)
+        end = monthlen(y, m) + 1
+        for d in range(end-days_before, end):
+            yield y, m, d
+        for d in range(1, ndays + 1):
+            yield year, month, d
+        y, m = nextmonth(year, month)
+        for d in range(1, days_after + 1):
+            yield y, m, d
+
+    def itermonthdays4(self, year, month):
+        """
+        Like itermonthdates(), but will yield (year, month, day, day_of_week) tuples.
+        Can be used for dates outside of datetime.date range.
+        """
+        for i, (y, m, d) in enumerate(self.itermonthdays3(year, month)):
+            yield y, m, d, (self.firstweekday + i) % 7
+
     def monthdatescalendar(self, year, month):
         """
         Return a matrix (list of lists) representing a month's calendar.
diff --git a/Lib/test/test_calendar.py b/Lib/test/test_calendar.py
index c777f648356..ad8b6bb6b93 100644
--- a/Lib/test/test_calendar.py
+++ b/Lib/test/test_calendar.py
@@ -502,10 +502,15 @@ class CalendarTestCase(unittest.TestCase):
         new_october = calendar.TextCalendar().formatmonthname(2010, 10, 10)
         self.assertEqual(old_october, new_october)
 
-    def test_itermonthdates(self):
-        # ensure itermonthdates doesn't overflow after datetime.MAXYEAR
-        # see #15421
-        list(calendar.Calendar().itermonthdates(datetime.MAXYEAR, 12))
+    def test_itermonthdays3(self):
+        # ensure itermonthdays3 doesn't overflow after datetime.MAXYEAR
+        list(calendar.Calendar().itermonthdays3(datetime.MAXYEAR, 12))
+
+    def test_itermonthdays4(self):
+        cal = calendar.Calendar(firstweekday=3)
+        days = list(cal.itermonthdays4(2001, 2))
+        self.assertEqual(days[0], (2001, 2, 1, 3))
+        self.assertEqual(days[-1], (2001, 2, 28, 2))
 
     def test_itermonthdays(self):
         for firstweekday in range(7):
@@ -846,7 +851,8 @@ class MiscTestCase(unittest.TestCase):
         blacklist = {'mdays', 'January', 'February', 'EPOCH',
                      'MONDAY', 'TUESDAY', 'WEDNESDAY', 'THURSDAY', 'FRIDAY',
                      'SATURDAY', 'SUNDAY', 'different_locale', 'c',
-                     'prweek', 'week', 'format', 'formatstring', 'main'}
+                     'prweek', 'week', 'format', 'formatstring', 'main',
+                     'monthlen', 'prevmonth', 'nextmonth'}
         support.check__all__(self, calendar, blacklist=blacklist)
 
 
diff --git a/Misc/NEWS.d/next/Library/2017-10-23-20-03-36.bpo-28292.1Gkim2.rst b/Misc/NEWS.d/next/Library/2017-10-23-20-03-36.bpo-28292.1Gkim2.rst
new file mode 100644
index 00000000000..e0eb53ea51c
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2017-10-23-20-03-36.bpo-28292.1Gkim2.rst
@@ -0,0 +1,5 @@
+Calendar.itermonthdates() will now consistently raise an exception when a
+date falls outside of the 0001-01-01 through 9999-12-31 range.  To support
+applications that cannot tolerate such exceptions, the new methods
+itermonthdays3() and itermonthdays4() are added.  The new methods return
+tuples and are not restricted by the range supported by datetime.date.