diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 6b21bed..80bc291 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -204,7 +204,13 @@
         self.extMatch = re.compile(self.extMatch)
         self.interval = self.interval * interval # multiply by units requested
         self.rolloverAt = currentTime + self.interval
+        # If we are rolling over at midnight or weekly, then the interval is already known.
+        # What we need to figure out is WHEN the next interval is.
+        self.adjustRollover(currentTime)
 
+        #print "Will rollover at %d, %d seconds from now" % (self.rolloverAt, self.rolloverAt - currentTime)
+
+    def adjustRollover(self, currentTime):
         # If we are rolling over at midnight or weekly, then the interval is already known.
         # What we need to figure out is WHEN the next interval is.  In other words,
         # if you are rolling over at midnight, then your base interval is 1 day,
@@ -214,7 +220,7 @@
         # the rest.  Note that this code doesn't care about leap seconds. :)
         if self.when == 'MIDNIGHT' or self.when.startswith('W'):
             # This could be done with less code, but I wanted it to be clear
-            if utc:
+            if self.utc:
                 t = time.gmtime(currentTime)
             else:
                 t = time.localtime(currentTime)
@@ -240,7 +246,7 @@
             # The calculations described in 2) and 3) above need to have a day added.
             # This is because the above time calculation takes us to midnight on this
             # day, i.e. the start of the next day.
-            if when.startswith('W'):
+            if self.when.startswith('W'):
                 day = t[6] # 0 is Monday
                 if day != self.dayOfWeek:
                     if day < self.dayOfWeek:
@@ -248,7 +254,7 @@
                     else:
                         daysToWait = 6 - day + self.dayOfWeek + 1
                     newRolloverAt = self.rolloverAt + (daysToWait * (60 * 60 * 24))
-                    if not utc:
+                    if not self.utc:
                         dstNow = t[-1]
                         dstAtRollover = time.localtime(newRolloverAt)[-1]
                         if dstNow != dstAtRollover:
@@ -258,8 +264,6 @@
                                 newRolloverAt = newRolloverAt + 3600
                     self.rolloverAt = newRolloverAt
 
-        #print "Will rollover at %d, %d seconds from now" % (self.rolloverAt, self.rolloverAt - currentTime)
-
     def shouldRollover(self, record):
         """
         Determine if rollover should occur.
@@ -341,6 +345,7 @@
                 else:           # DST bows out before next rollover, so we need to add an hour
                     newRolloverAt = newRolloverAt + 3600
         self.rolloverAt = newRolloverAt
+        self.adjustRollover(time.time())
 
 class WatchedFileHandler(logging.FileHandler):
     """
diff --git a/Misc/NEWS b/Misc/NEWS
index bc674ec..ffb15b4 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -317,6 +317,9 @@
 Library
 -------
 
+- Issue #5262: Fixed bug in next rollover time computation in
+  TimedRotatingFileHandler.
+
 - Issue #6263: Fixed syntax error in distutils.cygwincompiler.
 
 - Issue #5201: distutils.sysconfig.parse_makefile() now understands `$$`
@@ -351,7 +354,7 @@
 
 - Issue #1424152: Fix for httplib, urllib2 to support SSL while working through
   proxy. Original patch by Christopher Li, changes made by Senthil Kumaran.
- 
+
 - Issue #1983: Fix functions taking or returning a process identifier to use
   the dedicated C type ``pid_t`` instead of a C ``int``. Some platforms have
   a process identifier type wider than the standard C integer type.
@@ -359,7 +362,7 @@
 - Issue #4066: smtplib.SMTP_SSL._get_socket now correctly returns the socket.
   Patch by Farhan Ahmad, test by Marcin Bachry.
 
-- Issue #6062: In distutils, fixed the package option of build_ext. Feedback 
+- Issue #6062: In distutils, fixed the package option of build_ext. Feedback
   and tests on pywin32 by Tim Golden.
 
 - Issue #6053: Fixed distutils tests on win32. patch by Hirokazu Yamamoto.
@@ -367,7 +370,7 @@
 - Issue #6046: Fixed the library extension when distutils build_ext is used
   inplace. Initial patch by Roumen Petrov.
 
-- Issue #6041: Now distutils `sdist` and `register` commands use `check` as a 
+- Issue #6041: Now distutils `sdist` and `register` commands use `check` as a
   subcommand.
 
 - Issue #2116: Weak references and weak dictionaries now support copy()ing and
@@ -517,8 +520,8 @@
 
 - unittest.assertNotEqual() now uses the inequality operator (!=) instead
   of the equality operator.
-  
-- Issue #6001: Test discovery for unittest. Implemented in 
+
+- Issue #6001: Test discovery for unittest. Implemented in
   unittest.TestLoader.discover and from the command line.
 
 - Issue #5679: The methods unittest.TestCase.addCleanup and doCleanups were added.
@@ -528,11 +531,11 @@
 
 - Issue #3379: unittest.main now takes an optional exit argument. If False main
   doesn't call sys.exit allowing it to be used from the interactive interpreter.
-  
-- Issue #5995: unittest.main now takes an optional verbosity argument allowing 
+
+- Issue #5995: unittest.main now takes an optional verbosity argument allowing
   test modules to be run with a higher than default verbosity.
-  
-- Issue #5995: A fix to allow you to run "python -m unittest test_module" or 
+
+- Issue #5995: A fix to allow you to run "python -m unittest test_module" or
   "python -m unittest test_module.TestClass" from the command line.
 
 - Issue #5728: unittest.TestResult has new startTestRun and stopTestRun methods;