diff --git a/Doc/howto/logging-cookbook.rst b/Doc/howto/logging-cookbook.rst
index 7dc8021..37b2f29 100644
--- a/Doc/howto/logging-cookbook.rst
+++ b/Doc/howto/logging-cookbook.rst
@@ -1102,3 +1102,31 @@
 For more information about this configuration, you can see the `relevant
 section <https://docs.djangoproject.com/en/1.3/topics/logging/#configuring-logging>`_
 of the Django documentation.
+
+.. _cookbook-rotator-namer:
+
+Using a rotator and namer to customise log rotation processing
+--------------------------------------------------------------
+
+An example of how you can define a namer and rotator is given in the following
+snippet, which shows zlib-based compression of the log file::
+
+    def namer(name):
+        return name + ".gz"
+
+    def rotator(source, dest):
+        with open(source, "rb") as sf:
+            data = sf.read()
+            compressed = zlib.compress(data, 9)
+            with open(dest, "wb") as df:
+                df.write(compressed)
+        os.remove(source)
+
+    rh = logging.handlers.RotatingFileHandler(...)
+    rh.rotator = rotator
+    rh.namer = namer
+
+These are not “true” .gz files, as they are bare compressed data, with no
+“container” such as you’d find in an actual gzip file. This snippet is just
+for illustration purposes.
+
diff --git a/Doc/library/logging.handlers.rst b/Doc/library/logging.handlers.rst
index 3911d4d..183d5f9 100644
--- a/Doc/library/logging.handlers.rst
+++ b/Doc/library/logging.handlers.rst
@@ -164,6 +164,87 @@
       changed.  If it has, the existing stream is flushed and closed and the
       file opened again, before outputting the record to the file.
 
+.. _base-rotating-handler:
+
+BaseRotatingHandler
+^^^^^^^^^^^^^^^^^^^
+
+The :class:`BaseRotatingHandler` class, located in the :mod:`logging.handlers`
+module, is the base class for the rotating file handlers,
+:class:`RotatingFileHandler` and :class:`TimedRotatingFileHandler`. You should
+not need to instantiate this class, but it has attributes and methods you may
+need to override.
+
+.. class:: BaseRotatingHandler(filename, mode, encoding=None, delay=False)
+
+   The parameters are as for :class:`FileHandler`. The attributes are:
+
+   .. attribute:: namer
+
+      If this attribute is set to a callable, the :meth:`rotation_filename`
+      method delegates to this callable. The parameters passed to the callable
+      are those passed to :meth:`rotation_filename`.
+
+      .. note:: The namer function is called quite a few times during rollover,
+         so it should be as simple and as fast as possible. It should also
+         return the same output every time for a given input, otherwise the
+         rollover behaviour may not work as expected.
+
+      .. versionadded:: 3.3
+
+
+   .. attribute:: BaseRotatingHandler.rotator
+
+      If this attribute is set to a callable, the :meth:`rotate` method
+      delegates to this callable.  The parameters passed to the callable are
+      those passed to :meth:`rotate`.
+
+      .. versionadded:: 3.3
+
+   .. method:: BaseRotatingHandler.rotation_filename(default_name)
+
+      Modify the filename of a log file when rotating.
+
+      This is provided so that a custom filename can be provided.
+
+      The default implementation calls the 'namer' attribute of the handler,
+      if it's callable, passing the default name to it. If the attribute isn't
+      callable (the default is `None`), the name is returned unchanged.
+
+      :param default_name: The default name for the log file.
+
+      .. versionadded:: 3.3
+
+
+   .. method:: BaseRotatingHandler.rotate(source, dest)
+
+      When rotating, rotate the current log.
+
+      The default implementation calls the 'rotator' attribute of the handler,
+      if it's callable, passing the source and dest arguments to it. If the
+      attribute isn't callable (the default is `None`), the source is simply
+      renamed to the destination.
+
+      :param source: The source filename. This is normally the base
+                     filename, e.g. 'test.log'
+      :param dest:   The destination filename. This is normally
+                     what the source is rotated to, e.g. 'test.log.1'.
+
+      .. versionadded:: 3.3
+
+The reason the attributes exist is to save you having to subclass - you can use
+the same callables for instances of :class:`RotatingFileHandler` and
+:class:`TimedRotatingFileHandler`. If either the namer or rotator callable
+raises an exception, this will be handled in the same way as any other
+exception during an :meth:`emit` call, i.e. via the :meth:`handleError` method
+of the handler.
+
+If you need to make more significant changes to rotation processing, you can
+override the methods.
+
+For an example, see :ref:`cookbook-rotator-namer`.
+
+
 .. _rotating-file-handler:
 
 RotatingFileHandler
diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 52e18e5..822b4ef 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -52,13 +52,15 @@
     Not meant to be instantiated directly.  Instead, use RotatingFileHandler
     or TimedRotatingFileHandler.
     """
-    def __init__(self, filename, mode, encoding=None, delay=0):
+    def __init__(self, filename, mode, encoding=None, delay=False):
         """
         Use the specified filename for streamed logging
         """
         logging.FileHandler.__init__(self, filename, mode, encoding, delay)
         self.mode = mode
         self.encoding = encoding
+        self.namer = None
+        self.rotator = None
 
     def emit(self, record):
         """
@@ -76,12 +78,50 @@
         except:
             self.handleError(record)
 
+    def rotation_filename(self, default_name):
+        """
+        Modify the filename of a log file when rotating.
+
+        This is provided so that a custom filename can be provided.
+
+        The default implementation calls the 'namer' attribute of the
+        handler, if it's callable, passing the default name to
+        it. If the attribute isn't callable (the default is None), the name
+        is returned unchanged.
+
+        :param default_name: The default name for the log file.
+        """
+        if not callable(self.namer):
+            result = default_name
+        else:
+            result = self.namer(default_name)
+        return result
+
+    def rotate(self, source, dest):
+        """
+        When rotating, rotate the current log.
+
+        The default implementation calls the 'rotator' attribute of the
+        handler, if it's callable, passing the source and dest arguments to
+        it. If the attribute isn't callable (the default is None), the source
+        is simply renamed to the destination.
+
+        :param source: The source filename. This is normally the base
+                       filename, e.g. 'test.log'
+        :param dest:   The destination filename. This is normally
+                       what the source is rotated to, e.g. 'test.log.1'.
+        """
+        if not callable(self.rotator):
+            os.rename(source, dest)
+        else:
+            self.rotator(source, dest)
+
 class RotatingFileHandler(BaseRotatingHandler):
     """
     Handler for logging to a set of files, which switches from one file
     to the next when the current file reaches a certain size.
     """
-    def __init__(self, filename, mode='a', maxBytes=0, backupCount=0, encoding=None, delay=0):
+    def __init__(self, filename, mode='a', maxBytes=0, backupCount=0, encoding=None, delay=False):
         """
         Open the specified file and use it as the stream for logging.
 
@@ -122,16 +162,17 @@
             self.stream = None
         if self.backupCount > 0:
             for i in range(self.backupCount - 1, 0, -1):
-                sfn = "%s.%d" % (self.baseFilename, i)
-                dfn = "%s.%d" % (self.baseFilename, i + 1)
+                sfn = self.rotation_filename("%s.%d" % (self.baseFilename, i))
+                dfn = self.rotation_filename("%s.%d" % (self.baseFilename,
+                                                        i + 1))
                 if os.path.exists(sfn):
                     if os.path.exists(dfn):
                         os.remove(dfn)
                     os.rename(sfn, dfn)
-            dfn = self.baseFilename + ".1"
+            dfn = self.rotation_filename(self.baseFilename + ".1")
             if os.path.exists(dfn):
                 os.remove(dfn)
-            os.rename(self.baseFilename, dfn)
+            self.rotate(self.baseFilename, dfn)
         self.mode = 'w'
         self.stream = self._open()
 
@@ -179,19 +220,19 @@
         if self.when == 'S':
             self.interval = 1 # one second
             self.suffix = "%Y-%m-%d_%H-%M-%S"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}$"
+            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}-\d{2}(\.\w+)?$"
         elif self.when == 'M':
             self.interval = 60 # one minute
             self.suffix = "%Y-%m-%d_%H-%M"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}$"
+            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}-\d{2}(\.\w+)?$"
         elif self.when == 'H':
             self.interval = 60 * 60 # one hour
             self.suffix = "%Y-%m-%d_%H"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}$"
+            self.extMatch = r"^\d{4}-\d{2}-\d{2}_\d{2}(\.\w+)?$"
         elif self.when == 'D' or self.when == 'MIDNIGHT':
             self.interval = 60 * 60 * 24 # one day
             self.suffix = "%Y-%m-%d"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}$"
+            self.extMatch = r"^\d{4}-\d{2}-\d{2}(\.\w+)?$"
         elif self.when.startswith('W'):
             self.interval = 60 * 60 * 24 * 7 # one week
             if len(self.when) != 2:
@@ -200,7 +241,7 @@
                 raise ValueError("Invalid day specified for weekly rollover: %s" % self.when)
             self.dayOfWeek = int(self.when[1])
             self.suffix = "%Y-%m-%d"
-            self.extMatch = r"^\d{4}-\d{2}-\d{2}$"
+            self.extMatch = r"^\d{4}-\d{2}-\d{2}(\.\w+)?$"
         else:
             raise ValueError("Invalid rollover interval specified: %s" % self.when)
 
@@ -323,10 +364,11 @@
             timeTuple = time.gmtime(t)
         else:
             timeTuple = time.localtime(t)
-        dfn = self.baseFilename + "." + time.strftime(self.suffix, timeTuple)
+        dfn = self.rotation_filename(self.baseFilename + "." +
+                                     time.strftime(self.suffix, timeTuple))
         if os.path.exists(dfn):
             os.remove(dfn)
-        os.rename(self.baseFilename, dfn)
+        self.rotate(self.baseFilename, dfn)
         if self.backupCount > 0:
             for s in self.getFilesToDelete():
                 os.remove(s)
@@ -367,7 +409,7 @@
     This handler is based on a suggestion and patch by Chad J.
     Schroeder.
     """
-    def __init__(self, filename, mode='a', encoding=None, delay=0):
+    def __init__(self, filename, mode='a', encoding=None, delay=False):
         logging.FileHandler.__init__(self, filename, mode, encoding, delay)
         if not os.path.exists(self.baseFilename):
             self.dev, self.ino = -1, -1
diff --git a/Lib/test/test_logging.py b/Lib/test/test_logging.py
index 5e192d5..7aa68ef 100644
--- a/Lib/test/test_logging.py
+++ b/Lib/test/test_logging.py
@@ -46,6 +46,7 @@
 import unittest
 import warnings
 import weakref
+import zlib
 try:
     import threading
     # The following imports are needed only for tests which
@@ -3587,15 +3588,61 @@
         rh.close()
 
     def test_rollover_filenames(self):
+        def namer(name):
+            return name + ".test"
         rh = logging.handlers.RotatingFileHandler(
             self.fn, backupCount=2, maxBytes=1)
+        rh.namer = namer
         rh.emit(self.next_rec())
         self.assertLogFile(self.fn)
         rh.emit(self.next_rec())
-        self.assertLogFile(self.fn + ".1")
+        self.assertLogFile(namer(self.fn + ".1"))
         rh.emit(self.next_rec())
-        self.assertLogFile(self.fn + ".2")
-        self.assertFalse(os.path.exists(self.fn + ".3"))
+        self.assertLogFile(namer(self.fn + ".2"))
+        self.assertFalse(os.path.exists(namer(self.fn + ".3")))
+        rh.close()
+
+    def test_rotator(self):
+        def namer(name):
+            return name + ".gz"
+
+        def rotator(source, dest):
+            with open(source, "rb") as sf:
+                data = sf.read()
+                compressed = zlib.compress(data, 9)
+                with open(dest, "wb") as df:
+                    df.write(compressed)
+            os.remove(source)
+
+        rh = logging.handlers.RotatingFileHandler(
+            self.fn, backupCount=2, maxBytes=1)
+        rh.rotator = rotator
+        rh.namer = namer
+        m1 = self.next_rec()
+        rh.emit(m1)
+        self.assertLogFile(self.fn)
+        m2 = self.next_rec()
+        rh.emit(m2)
+        fn = namer(self.fn + ".1")
+        self.assertLogFile(fn)
+        with open(fn, "rb") as f:
+            compressed = f.read()
+            data = zlib.decompress(compressed)
+            self.assertEqual(data.decode("ascii"), m1.msg + "\n")
+        rh.emit(self.next_rec())
+        fn = namer(self.fn + ".2")
+        self.assertLogFile(fn)
+        with open(fn, "rb") as f:
+            compressed = f.read()
+            data = zlib.decompress(compressed)
+            self.assertEqual(data.decode("ascii"), m1.msg + "\n")
+        rh.emit(self.next_rec())
+        fn = namer(self.fn + ".2")
+        with open(fn, "rb") as f:
+            compressed = f.read()
+            data = zlib.decompress(compressed)
+            self.assertEqual(data.decode("ascii"), m2.msg + "\n")
+        self.assertFalse(os.path.exists(namer(self.fn + ".3")))
         rh.close()
 
 class TimedRotatingFileHandlerTest(BaseFileTest):