diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -196,11 +196,12 @@
     If backupCount is > 0, when rollover is done, no more than backupCount
     files are kept - the oldest ones are deleted.
     """
-    def __init__(self, filename, when='h', interval=1, backupCount=0, encoding=None, delay=False, utc=False):
+    def __init__(self, filename, when='h', interval=1, backupCount=0, encoding=None, delay=False, utc=False, atTime=None):
         BaseRotatingHandler.__init__(self, filename, 'a', encoding, delay)
         self.when = when.upper()
         self.backupCount = backupCount
         self.utc = utc
+        self.atTime = atTime
         # Calculate the real rollover interval, which is just the number of
         # seconds between rollovers.  Also set the filename suffix used when
         # a rollover occurs.  Current 'when' events supported:
@@ -270,9 +271,22 @@
             currentHour = t[3]
             currentMinute = t[4]
             currentSecond = t[5]
-            # r is the number of seconds left between now and midnight
-            r = _MIDNIGHT - ((currentHour * 60 + currentMinute) * 60 +
-                    currentSecond)
+            currentDay = t[6]
+            # r is the number of seconds left between now and the next rotation
+            if self.atTime is None:
+                rotate_ts = _MIDNIGHT
+            else:
+                rotate_ts = ((self.atTime.hour * 60 + self.atTime.minute)*60 +
+                    self.atTime.second)
+
+            r = rotate_ts - ((currentHour * 60 + currentMinute) * 60 +
+                currentSecond)
+            if r < 0:
+                # Rotate time is before the current time (for example when
+                # self.rotateAt is 13:45 and it now 14:15), rotation is 
+                # tomorrow.
+                r += _MIDNIGHT
+                currentDay = (currentDay + 1) % 7
             result = currentTime + r
             # If we are rolling over on a certain day, add in the number of days until
             # the next rollover, but offset by 1 since we just calculated the time
@@ -290,7 +304,7 @@
             # This is because the above time calculation takes us to midnight on this
             # day, i.e. the start of the next day.
             if self.when.startswith('W'):
-                day = t[6] # 0 is Monday
+                day = currentDay # 0 is Monday
                 if day != self.dayOfWeek:
                     if day < self.dayOfWeek:
                         daysToWait = self.dayOfWeek - day
@@ -307,6 +321,7 @@
                                 addend = 3600
                             newRolloverAt += addend
                     result = newRolloverAt
+
         return result
 
     def shouldRollover(self, record):
diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -3834,6 +3834,21 @@
         assertRaises(ValueError, logging.handlers.TimedRotatingFileHandler,
                      self.fn, 'W7', delay=True)
 
+    def test_compute_rollover_daily_attime(self):
+        currentTime = 0
+        atTime = datetime.time(12, 0, 0)
+        rh = logging.handlers.TimedRotatingFileHandler(
+            self.fn, when='MIDNIGHT', interval=1, backupCount=0, utc=True, atTime=atTime)
+
+        actual = rh.computeRollover(currentTime)
+        self.assertEqual(actual, currentTime + 12 * 60 * 60)
+
+        actual = rh.computeRollover(currentTime + 13 * 60 * 60)
+        self.assertEqual(actual, currentTime + 36 * 60 * 60)
+
+        rh.close()
+
+
 def secs(**kw):
     return datetime.timedelta(**kw) // datetime.timedelta(seconds=1)